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adj
- (linear algebra, of matrix) Having no inverse.
- (linear algebra, of transformation) Having the property that the matrix of coefficients of the new variables has a determinant equal to zero.
- Being the only one of the kind; unique.
- Being only one of a larger population; single, individual.
- (set theory, of a cardinal number) Not equal to its own cofinality.
- Distinguished by superiority: peerless, unmatched, eminent, exceptional, extraordinary.
- (chiefly law) Each; individual.
- (grammar) Referring to only one thing or person.
- Out of the ordinary; curious.
- unusual or striking
- the single one of its kind
- being a single and separate person or thing
- beyond or deviating from the usual or expected
- grammatical number category referring to a single item or unit
- composed of one member, set, or kind
noun
noun
- (linear algebra) For a given square matrix M over some field K, the smallest-degree monic polynomial over K which, when applied to M, yields the zero matrix.
- (field theory) Given an algebraic element α of a given extension field of some field K, the monic polynomial of smallest degree of which α is a root.
adj
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
- (linear algebra, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
- (module theory, of a module) In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
- (representation theory, of a linear representation of a group or algebra) Being a direct sum of simple representations (also known as irreducible representations).
- (ring theory, of an algebra or ring) Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
- (category theory, most generally, of an abelian category) Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
- (Lie theory, of a Lie algebra) Being a direct sum of simple Lie algebras.
- (group theory, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial.
- (of a ring, somewhat proscribed) Semiprimitive: having trivial Jacobson radical.
adj
- (linear algebra) Said of a real, square matrix: that the product of it with a column vector on its right side and the transpose of that column vector on its left side is greater or equal to zero, only equaling zero if the vector itself is zero.
- (linear algebra) Said of a quadratic form: that the application of it to a tuple is greater or equal to zero, only equaling zero if the tuple itself is zero.
noun
- (linear algebra) The number of elements of any basis of a vector space.
- (computing) Any of the independent ranges of indices in a multidimensional array.
- A construct whereby objects or individuals can be distinguished.
- (physics) One of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.
- (geometry) The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates.
- (science fiction, fantasy) A universe or plane of existence.
- A single aspect of a given thing.
- A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.
- the magnitude of something in a particular direction (especially length or width or height)
- a construct whereby objects or individuals can be distinguished
- one of three Cartesian coordinates that determine a position in space
- magnitude or extent
verb
adj
noun
- A level or rank in an organization, profession, or society.
- (military) A formation of troops, ships, aircraft, etc., in diagonal parallel rows.
- (cycling) A line of riders seeking maximum drafting in a crosswind, resulting in a diagonal line across the road.
- a diffraction grating consisting of a pile of plates of equal thickness arranged stepwise with a constant offset
- status in a society or organization
- a body of troops arranged in a line
verb
noun
- (linear algebra) A term at any position in a matrix.
- (Midlands) A passageway between terraced houses that provides a means of entering a back garden or yard.
- (uncountable) Permission to enter.
- A small group formed within a church, especially Episcopal, for simple dinner and fellowship, and to help facilitate new friendships
- A record made in a log, diary or anything similarly organized; (computing) a datum in a database.
- The act of entering.
- A doorway that provides a means of entering a building.
- An item in a list, such as an article in a dictionary or encyclopedia.
- The exhibition or depositing of a ship's papers at the customhouse, to procure licence to land goods; or the giving an account of a ship's cargo to the officer of the customs, and obtaining his permission to land the goods.
- (hunting) The introduction of new hounds into a pack.
- (insurance) The start of an insurance contract.
- (law) The act of taking possession.
- A small room immediately inside the front door of a house or other building, often having an access to a stairway and leading on to other rooms
- (music) The point when a musician starts to play or sing; entrance.
- something that provides access (to get in or get out)
- something (manuscripts or architectural plans and models or estimates or works of art of all genres etc.) submitted for the judgment of others (as in a competition)
- an item inserted in a written record
- the act of beginning something new
- the act of entering
- a written record of a commercial transaction
noun
- (mathematics, linear algebra) The set of eigenvalues of a matrix.
- (psychology, education, usually with the) The autism spectrum.
- Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
- (mathematics, functional analysis) Of a bounded linear operator A, the set of scalar values λ such that the operator A—λI, where I denotes the identity operator, does not have a bounded inverse; intended as a generalisation of the linear algebra sense.
- A range; a continuous, infinite, one-dimensional set, possibly bounded by extremes.
- The image of something seen that persists after the eyes are closed.
- (chemistry) The pattern of absorption or emission of radiation produced by a substance when subjected to energy (radiation, heat, electricity, etc.).
- (commutative algebra, algebraic geometry) An abstract object in mathematics created from a commutative ring R and denoted operatorname Spec(R) or operatorname SpecR and said to be the spectrum of R; useful in the study of such rings for providing a geometric object which encodes many of the properties R, and in modern geometry for generalizing the notion of an algebraic variety to that of an affine scheme. Formally, the set of all prime ideals R equipped with the Zariski topology and augmented with a sheaf of rings called the structure sheaf, generated by the B-sheaf on the distinguished open sets D_f which assigns the localization of R at f to each set D_f, regarded as a ring of functions on D_f. See Spectrum of a ring on Wikipedia.Wikipedia
- an ordered array of the components of an emission or wave
- a broad range of related objects or values or qualities or ideas or activities
noun
- (linear algebra) A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.
- (mathematics) coproduct in some categories, like abelian groups, topological spaces or modules
- (linear algebra) A linear sum in which the intersection of the summands has dimension zero. Equivalently, a linear sum of two subspaces, any vector of which can be expressed uniquely as a sum of two vectors: one vector belonging to the first subspace, and the other vector belonging to the second subspace.
- a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets
noun
adj
- (linear algebra, of a function in two variables) Linear (preserving linear combinations) in each variable.
- (complex analysis, physics, engineering) Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).
- linear with respect to each of two variables or positions
noun
- (algebra) A non-zero commutative ring in which all non-zero elements are invertible; a simple commutative ring.
- (computing, object-oriented programming) An area of memory or storage reserved for a particular value, subject to virtual access controls.
- A place where competitive matches are carried out with figures, or playing area in a board game or a computer game.
- A wide, open space that is used to grow crops or to hold farm animals, usually enclosed by a fence, hedge or other barrier.
- (baseball) The outfield.
- (usually in the plural) The open country near or belonging to a town or city.
- A section of a form which is supposed to be filled with data.
- An airfield, airport or air base; especially, one with unpaved runways.
- A domain of study, knowledge or practice.
- (vexillology) The background of the flag.
- A place where a battle is fought; a battlefield.
- (numismatics) The part of a coin left unoccupied by the main device.
- A component of a database in which a single unit of information is stored.
- A land area free of woodland, cities, and towns; an area of open country.
- (geology) A region containing a particular mineral.
- The extent of a given perception.
- (heraldry) The background of the shield.
- (physics) A physical phenomenon (such as force, potential or fluid velocity) that pervades a region; a mathematical model of such a phenomenon that associates each point and time with a scalar, vector or tensor quantity.
- A competitive situation, circumstance in which one faces conflicting moves of rivals.
- A realm of practical, direct or natural operation, contrasted with an office, classroom, or laboratory.
- (electronics, film, animation) Part (usually one half) of a frame in an interlaced signal.
- (metonymic) All of the competitors in any outdoor contest or trial, or all except the favourites in the betting.
- An area reserved for playing a game or race with one’s physical force.
- An unrestricted or favourable opportunity for action, operation, or achievement.
- (mathematics) a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1
- the area that is visible (as through an optical instrument)
- a piece of land cleared of trees and usually enclosed
- a region in which active military operations are in progress
- a place where planes take off and land
- (computer science) a set of one or more adjacent characters comprising a unit of information
- somewhere (away from a studio or office or library or laboratory) where practical work is done or data is collected
- extensive tract of level open land
- a piece of land prepared for playing a game
- all of the horses in a particular horse race
- a region where a battle is being (or has been) fought
- a particular kind of commercial enterprise
- a geographic region (land or sea) under which something valuable is found
- a particular environment or walk of life
- the space around a radiating body within which its electromagnetic oscillations can exert force on another similar body not in contact with it
- a branch of knowledge
- all the competitors in a particular contest or sporting event
verb
- (transitive) To answer; to address.
- (transitive, sports) To place (a team, its players, etc.) in a game.
- (transitive) To execute research (in the field).
- (transitive, military) To deploy in the field.
- (transitive, sports) To intercept or catch (a ball) and play it.
- (intransitive, baseball, softball, cricket, and other batting sports) To be the team catching and throwing the ball, as opposed to hitting it.
- select (a team or individual player) for a game
- play as a fielder
- catch or pick up (balls) in baseball or cricket
- answer adequately or successfully
noun
adj
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
noun
- (linear algebra, combinatorics) Given an n×n matrix a_ij,, the sum over all permutations π, of ∏ᵢ₌₁ⁿa_iπ(i).
- (collectible card games) A card whose effects persist beyond the turn on which it is played.
- A chemical hair treatment imparting or removing curliness, whose effects typically last for a period of weeks; a perm.
- a series of waves in the hair made by applying heat and chemicals
adj
adj
- (algebra, by extension, of two or more polynomials) Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).
- (number theory, of a positive integer) Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.
- (number theory, of two or more positive integers) Having no positive integer factors in common, aside from 1.
- (ring theory, by extension) (of two or more ideals of a ring) Whose sum is the whole ring; (of two or more elements of a ring) generating the whole ring.
noun
- (mathematics, linear algebra) Matrix similarity by an orthogonal matrix.
- (universal algebra) Any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.
- (mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.
- (psychology) A well-adjusted state or condition in which people are not lying to themselves or in denial.
- (mathematics, number theory) A relation between two numbers indicating they give the same remainder when divided by some given number.
- The quality of agreeing or corresponding; being suitable and appropriate.
- the quality of agreeing; being suitable and appropriate
noun
- (algebra) More generally, any of a set of irrational or complex numbers that are zeros of the same polynomial with integral coefficients.
- (mathematics) An explementary angle.
- (algebra, of a complex number) A complex conjugate.
- (grammar) A word agreeing in derivation with another word, and therefore generally resembling it in meaning.
- (algebra, field theory, of an element of an extension field) Given a field extension L / K and an element α ∈ L, any other element β ∈ L that is another root of the minimal polynomial of α over K.
- (anatomy, obstetrics) A type of pelvic measurement.
- Any entity formed by joining two or more smaller entities together.
- (immunology) A weak and a strong antigen covalently linked together
- a mixture of two partially miscible liquids A and B produces two conjugate solutions: one of A in B and another of B in A
adj
- (grammar) Agreeing in derivation and radical signification; said of words.
- (botany) In single pairs; coupled.
- (chemistry) Containing two or more radicals supposed to act the part of a single one.
- United in pairs; yoked together; coupled.
- (mathematics) Presenting themselves simultaneously and having reciprocal properties; said of quantities, points, lines, axes, curves, etc.
- (of a pinnate leaflet) having only one pair of leaflets
- formed by the union of two compounds
- of an organic compound; containing two or more double bonds each separated from the other by a single bond
- joined together especially in a pair or pairs
verb
- (rare) To join together, to unite; to juxtapose.
- (biology, of bacteria and algae) To temporarily fuse, exchanging or transferring DNA.
- (grammar, transitive) To inflect (a verb) for each person, in order, for one or more tenses; to list or recite its principal parts.
- (mathematics) To multiply on the left by one element and on the right by its inverse.
- unite chemically so that the product is easily broken down into the original compounds
- undergo conjugation
- add inflections showing person, number, gender, tense, aspect, etc.
noun
- (mathematics) A matrix.
- A group of hedgehogs.
- Order; a regular and imposing arrangement; disposition in regular lines; hence, order of battle.
- Clothing and ornamentation; raiment.
- A large collection.
- A microarray.
- (military) A militia.
- (programming) Any of various data structures designed to hold multiple elements of the same type; especially, a data structure that holds these elements in adjacent memory locations so that they may be retrieved using numeric indices.
- An orderly series, arrangement or sequence.
- (law) A ranking or setting forth in order, by the proper officer, of a jury as impanelled in a cause; the panel itself; or the whole body of jurors summoned to attend the court.
- A collection laid out to be viewed in full.
- an arrangement of aerials spaced to give desired directional characteristics
- an orderly arrangement
- especially fine or decorative clothing
- an impressive display
verb
- To clothe and ornament; to adorn or attire.
- To lay out in an orderly arrangement; to deploy or marshal.
- (law) To set in order, as a jury, for the trial of a cause; that is, to call them one at a time.
- lay out orderly or logically in a line or as if in a line
- align oneself with a group or a way of thinking
noun
- (mathematical analysis) A zero (of an equation).
- (slang) A penis, especially the base of a penis.
- The part of a plant, generally underground, that anchors and supports the plant body, absorbs and stores water and nutrients, and in some plants is able to perform vegetative reproduction.
- (arithmetic) Of a number or expression, a number which, when raised to a specified power, yields the specified number or expression.
- (computing) The highest directory of a directory structure which may contain both files and subdirectories.
- (Australia, New Zealand, vulgar, slang) An act of sexual intercourse.
- (aviation) The section of a wing immediately adjacent to the fuselage.
- (music) The fundamental tone of any chord; the tone from whose harmonics, or overtones, a chord is composed.
- (arithmetic) A square root (understood if no power is specified; in which case, "the root of" is often abbreviated to "root").
- The part of a hair near the skin that has not been dyed, permed, or otherwise treated.
- (figurative) The primary source; origin.
- (graph theory, computing) The single node of a tree that has no parent.
- (engineering) The bottom of the thread of a threaded object.
- (computing) In UNIX terminology, the first user account with complete access to the operating system and its configuration, found at the root of the directory structure; the person who manages accounts on a UNIX system.
- The part of a tooth extending into the bone holding the tooth in place.
- An act of rummaging or searching.
- (Australia, New Zealand, vulgar, slang) A sexual partner.
- A root vegetable.
- (linguistic morphology) The primary lexical unit of a word, which carries the most significant aspects of semantic content and cannot be reduced into smaller constituents. Inflectional stems often derive from roots.
- (linguistics) A word from which another word or words are derived.
- The part of a hair under the skin that holds the hair in place.
- The lowest place, position, or part.
- a number that, when multiplied by itself some number of times, equals a given number
- the place where something begins, where it springs into being
- (botany) the usually underground organ that lacks buds or leaves or nodes; absorbs water and mineral salts; usually it anchors the plant to the ground
- a simple form inferred as the common basis from which related words in several languages can be derived by linguistic processes
- the set of values that give a true statement when substituted into an equation
- (linguistics) the form of a word after all affixes are removed
- the embedded part of a bodily structure such as a tooth, nail, or hair
- someone from whom you are descended (but usually more remote than a grandparent)
verb
- To fix firmly; to establish.
- (by extension) To seek favour or advancement by low arts or grovelling servility; to fawn.
- To grow roots; to enter the earth, as roots; to take root and begin to grow.
- (intransitive, with "for" or "on", US) To cheer (on); to show support (for) and hope for the success of. (See root for.)
- (transitive) To root out; to abolish.
- (intransitive) To rummage; to search as if by digging in soil.
- (computing slang, transitive) To get root or privileged access on (a computer system or mobile phone), often through bypassing some security mechanism.
- (Australia, New Zealand, Ireland, vulgar, slang) To sexually penetrate.
- (intransitive) Of a baby: to turn the head and open the mouth in search of food.
- (ambitransitive) To turn up or dig with the snout.
- (equestrianism, of a horse) To tug or pull at the reins aggressively by driving the head downwards while wearing a bit.
- To prepare, oversee, or otherwise cause the rooting of cuttings.
- cheer for
- become settled or established and stable in one's residence or life style
- come into existence, originate
- cause to take roots
- take root and begin to grow
- plant by the roots
- dig with the snout
adj
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
noun
name
noun
- (linear algebra) The sum of the diagonal elements of a square matrix.
- (engineering) A connecting bar or rod, pivoted at each end to the end of another piece, for transmitting motion, especially from one plane to another; specifically, such a piece in an organ stop action to transmit motion from the trundle to the lever actuating the stop slider.
- An enquiry sent out for a missing article, such as a letter or an express package.
- A mark left as a sign of passage of a person or animal.
- An act of tracing.
- (meteorology) A small amount of rain, not enough to be measured.
- (semiotics) A signifier approximated in the absence of stable signified.
- A very small amount, often residual, of some substance or material.
- An informal road or prominent path in an arid area.
- (programming) A sequence of instructions, including branches but not loops, that is executed for some input data.
- (electronics) A current-carrying conductive pathway on a printed circuit board.
- (fortification) The ground plan of a work or works.
- (grammar) An empty category occupying a position in the syntactic structure from which something has been moved, used to explain constructions such as wh-movement and the passive.
- (geometry) The intersection of a plane of projection, or an original plane, with a coordinate plane.
- One of two straps, chains, or ropes of a harness, extending from the collar or breastplate to a whippletree attached to a vehicle or thing to be drawn; a tug.
- a just detectable amount
- a visible mark (as a footprint) left by the passage of person or animal or vehicle
- either of two lines that connect a horse's harness to a wagon or other vehicle or to a whiffletree
- a drawing created by superimposing a semitransparent sheet of paper on the original image and copying on it the lines of the original image
- an indication that something has been present
- a suggestion of some quality
adj
verb
- (transitive) To draw or sketch lightly or with care.
- (computing, transitive) To follow the execution of the program by making it to stop after every instruction, or by making it print a message after every step.
- (transitive) To follow the trail of.
- To follow the history of.
- (transitive) To copy onto a sheet of paper superimposed over the original, by drawing over its lines.
- make a mark or lines on a surface
- pursue or chase relentlessly
- follow, discover, or ascertain the course of development of something
- make one's course or travel along a path; travel or pass over, around, or along
- copy by following the lines of the original drawing on a transparent sheet placed upon it; make a tracing of
- read with difficulty
- to go back over again
- discover traces of
noun
- (linear algebra) For a given square matrix M over some field K, the smallest-degree monic polynomial over K which, when applied to M, yields the zero matrix.
- (field theory) Given an algebraic element α of a given extension field of some field K, the monic polynomial of smallest degree of which α is a root.
noun
- (linear algebra) The number of elements of any basis of a vector space.
- (computing) Any of the independent ranges of indices in a multidimensional array.
- A construct whereby objects or individuals can be distinguished.
- (physics) One of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.
- (geometry) The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates.
- (science fiction, fantasy) A universe or plane of existence.
- A single aspect of a given thing.
- A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.
- the magnitude of something in a particular direction (especially length or width or height)
- a construct whereby objects or individuals can be distinguished
- one of three Cartesian coordinates that determine a position in space
- magnitude or extent
verb
noun
- (linear algebra) A term at any position in a matrix.
- (Midlands) A passageway between terraced houses that provides a means of entering a back garden or yard.
- (uncountable) Permission to enter.
- A small group formed within a church, especially Episcopal, for simple dinner and fellowship, and to help facilitate new friendships
- A record made in a log, diary or anything similarly organized; (computing) a datum in a database.
- The act of entering.
- A doorway that provides a means of entering a building.
- An item in a list, such as an article in a dictionary or encyclopedia.
- The exhibition or depositing of a ship's papers at the customhouse, to procure licence to land goods; or the giving an account of a ship's cargo to the officer of the customs, and obtaining his permission to land the goods.
- (hunting) The introduction of new hounds into a pack.
- (insurance) The start of an insurance contract.
- (law) The act of taking possession.
- A small room immediately inside the front door of a house or other building, often having an access to a stairway and leading on to other rooms
- (music) The point when a musician starts to play or sing; entrance.
- something that provides access (to get in or get out)
- something (manuscripts or architectural plans and models or estimates or works of art of all genres etc.) submitted for the judgment of others (as in a competition)
- an item inserted in a written record
- the act of beginning something new
- the act of entering
- a written record of a commercial transaction
noun
- (mathematics, linear algebra) The set of eigenvalues of a matrix.
- (psychology, education, usually with the) The autism spectrum.
- Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
- (mathematics, functional analysis) Of a bounded linear operator A, the set of scalar values λ such that the operator A—λI, where I denotes the identity operator, does not have a bounded inverse; intended as a generalisation of the linear algebra sense.
- A range; a continuous, infinite, one-dimensional set, possibly bounded by extremes.
- The image of something seen that persists after the eyes are closed.
- (chemistry) The pattern of absorption or emission of radiation produced by a substance when subjected to energy (radiation, heat, electricity, etc.).
- (commutative algebra, algebraic geometry) An abstract object in mathematics created from a commutative ring R and denoted operatorname Spec(R) or operatorname SpecR and said to be the spectrum of R; useful in the study of such rings for providing a geometric object which encodes many of the properties R, and in modern geometry for generalizing the notion of an algebraic variety to that of an affine scheme. Formally, the set of all prime ideals R equipped with the Zariski topology and augmented with a sheaf of rings called the structure sheaf, generated by the B-sheaf on the distinguished open sets D_f which assigns the localization of R at f to each set D_f, regarded as a ring of functions on D_f. See Spectrum of a ring on Wikipedia.Wikipedia
- an ordered array of the components of an emission or wave
- a broad range of related objects or values or qualities or ideas or activities
noun
- (linear algebra) A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.
- (mathematics) coproduct in some categories, like abelian groups, topological spaces or modules
- (linear algebra) A linear sum in which the intersection of the summands has dimension zero. Equivalently, a linear sum of two subspaces, any vector of which can be expressed uniquely as a sum of two vectors: one vector belonging to the first subspace, and the other vector belonging to the second subspace.
- a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets
noun
adj
- (linear algebra, of a function in two variables) Linear (preserving linear combinations) in each variable.
- (complex analysis, physics, engineering) Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).
- linear with respect to each of two variables or positions
noun
- (algebra) A non-zero commutative ring in which all non-zero elements are invertible; a simple commutative ring.
- (computing, object-oriented programming) An area of memory or storage reserved for a particular value, subject to virtual access controls.
- A place where competitive matches are carried out with figures, or playing area in a board game or a computer game.
- A wide, open space that is used to grow crops or to hold farm animals, usually enclosed by a fence, hedge or other barrier.
- (baseball) The outfield.
- (usually in the plural) The open country near or belonging to a town or city.
- A section of a form which is supposed to be filled with data.
- An airfield, airport or air base; especially, one with unpaved runways.
- A domain of study, knowledge or practice.
- (vexillology) The background of the flag.
- A place where a battle is fought; a battlefield.
- (numismatics) The part of a coin left unoccupied by the main device.
- A component of a database in which a single unit of information is stored.
- A land area free of woodland, cities, and towns; an area of open country.
- (geology) A region containing a particular mineral.
- The extent of a given perception.
- (heraldry) The background of the shield.
- (physics) A physical phenomenon (such as force, potential or fluid velocity) that pervades a region; a mathematical model of such a phenomenon that associates each point and time with a scalar, vector or tensor quantity.
- A competitive situation, circumstance in which one faces conflicting moves of rivals.
- A realm of practical, direct or natural operation, contrasted with an office, classroom, or laboratory.
- (electronics, film, animation) Part (usually one half) of a frame in an interlaced signal.
- (metonymic) All of the competitors in any outdoor contest or trial, or all except the favourites in the betting.
- An area reserved for playing a game or race with one’s physical force.
- An unrestricted or favourable opportunity for action, operation, or achievement.
- (mathematics) a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1
- the area that is visible (as through an optical instrument)
- a piece of land cleared of trees and usually enclosed
- a region in which active military operations are in progress
- a place where planes take off and land
- (computer science) a set of one or more adjacent characters comprising a unit of information
- somewhere (away from a studio or office or library or laboratory) where practical work is done or data is collected
- extensive tract of level open land
- a piece of land prepared for playing a game
- all of the horses in a particular horse race
- a region where a battle is being (or has been) fought
- a particular kind of commercial enterprise
- a geographic region (land or sea) under which something valuable is found
- a particular environment or walk of life
- the space around a radiating body within which its electromagnetic oscillations can exert force on another similar body not in contact with it
- a branch of knowledge
- all the competitors in a particular contest or sporting event
verb
- (transitive) To answer; to address.
- (transitive, sports) To place (a team, its players, etc.) in a game.
- (transitive) To execute research (in the field).
- (transitive, military) To deploy in the field.
- (transitive, sports) To intercept or catch (a ball) and play it.
- (intransitive, baseball, softball, cricket, and other batting sports) To be the team catching and throwing the ball, as opposed to hitting it.
- select (a team or individual player) for a game
- play as a fielder
- catch or pick up (balls) in baseball or cricket
- answer adequately or successfully
noun
adj
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
noun
- (linear algebra, combinatorics) Given an n×n matrix a_ij,, the sum over all permutations π, of ∏ᵢ₌₁ⁿa_iπ(i).
- (collectible card games) A card whose effects persist beyond the turn on which it is played.
- A chemical hair treatment imparting or removing curliness, whose effects typically last for a period of weeks; a perm.
- a series of waves in the hair made by applying heat and chemicals
adj
noun
- (mathematics, linear algebra) Matrix similarity by an orthogonal matrix.
- (universal algebra) Any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.
- (mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.
- (psychology) A well-adjusted state or condition in which people are not lying to themselves or in denial.
- (mathematics, number theory) A relation between two numbers indicating they give the same remainder when divided by some given number.
- The quality of agreeing or corresponding; being suitable and appropriate.
- the quality of agreeing; being suitable and appropriate
noun
- (algebra) More generally, any of a set of irrational or complex numbers that are zeros of the same polynomial with integral coefficients.
- (mathematics) An explementary angle.
- (algebra, of a complex number) A complex conjugate.
- (grammar) A word agreeing in derivation with another word, and therefore generally resembling it in meaning.
- (algebra, field theory, of an element of an extension field) Given a field extension L / K and an element α ∈ L, any other element β ∈ L that is another root of the minimal polynomial of α over K.
- (anatomy, obstetrics) A type of pelvic measurement.
- Any entity formed by joining two or more smaller entities together.
- (immunology) A weak and a strong antigen covalently linked together
- a mixture of two partially miscible liquids A and B produces two conjugate solutions: one of A in B and another of B in A
adj
- (grammar) Agreeing in derivation and radical signification; said of words.
- (botany) In single pairs; coupled.
- (chemistry) Containing two or more radicals supposed to act the part of a single one.
- United in pairs; yoked together; coupled.
- (mathematics) Presenting themselves simultaneously and having reciprocal properties; said of quantities, points, lines, axes, curves, etc.
- (of a pinnate leaflet) having only one pair of leaflets
- formed by the union of two compounds
- of an organic compound; containing two or more double bonds each separated from the other by a single bond
- joined together especially in a pair or pairs
verb
- (rare) To join together, to unite; to juxtapose.
- (biology, of bacteria and algae) To temporarily fuse, exchanging or transferring DNA.
- (grammar, transitive) To inflect (a verb) for each person, in order, for one or more tenses; to list or recite its principal parts.
- (mathematics) To multiply on the left by one element and on the right by its inverse.
- unite chemically so that the product is easily broken down into the original compounds
- undergo conjugation
- add inflections showing person, number, gender, tense, aspect, etc.
noun
- (mathematics) A matrix.
- A group of hedgehogs.
- Order; a regular and imposing arrangement; disposition in regular lines; hence, order of battle.
- Clothing and ornamentation; raiment.
- A large collection.
- A microarray.
- (military) A militia.
- (programming) Any of various data structures designed to hold multiple elements of the same type; especially, a data structure that holds these elements in adjacent memory locations so that they may be retrieved using numeric indices.
- An orderly series, arrangement or sequence.
- (law) A ranking or setting forth in order, by the proper officer, of a jury as impanelled in a cause; the panel itself; or the whole body of jurors summoned to attend the court.
- A collection laid out to be viewed in full.
- an arrangement of aerials spaced to give desired directional characteristics
- an orderly arrangement
- especially fine or decorative clothing
- an impressive display
verb
- To clothe and ornament; to adorn or attire.
- To lay out in an orderly arrangement; to deploy or marshal.
- (law) To set in order, as a jury, for the trial of a cause; that is, to call them one at a time.
- lay out orderly or logically in a line or as if in a line
- align oneself with a group or a way of thinking
noun
- (mathematical analysis) A zero (of an equation).
- (slang) A penis, especially the base of a penis.
- The part of a plant, generally underground, that anchors and supports the plant body, absorbs and stores water and nutrients, and in some plants is able to perform vegetative reproduction.
- (arithmetic) Of a number or expression, a number which, when raised to a specified power, yields the specified number or expression.
- (computing) The highest directory of a directory structure which may contain both files and subdirectories.
- (Australia, New Zealand, vulgar, slang) An act of sexual intercourse.
- (aviation) The section of a wing immediately adjacent to the fuselage.
- (music) The fundamental tone of any chord; the tone from whose harmonics, or overtones, a chord is composed.
- (arithmetic) A square root (understood if no power is specified; in which case, "the root of" is often abbreviated to "root").
- The part of a hair near the skin that has not been dyed, permed, or otherwise treated.
- (figurative) The primary source; origin.
- (graph theory, computing) The single node of a tree that has no parent.
- (engineering) The bottom of the thread of a threaded object.
- (computing) In UNIX terminology, the first user account with complete access to the operating system and its configuration, found at the root of the directory structure; the person who manages accounts on a UNIX system.
- The part of a tooth extending into the bone holding the tooth in place.
- An act of rummaging or searching.
- (Australia, New Zealand, vulgar, slang) A sexual partner.
- A root vegetable.
- (linguistic morphology) The primary lexical unit of a word, which carries the most significant aspects of semantic content and cannot be reduced into smaller constituents. Inflectional stems often derive from roots.
- (linguistics) A word from which another word or words are derived.
- The part of a hair under the skin that holds the hair in place.
- The lowest place, position, or part.
- a number that, when multiplied by itself some number of times, equals a given number
- the place where something begins, where it springs into being
- (botany) the usually underground organ that lacks buds or leaves or nodes; absorbs water and mineral salts; usually it anchors the plant to the ground
- a simple form inferred as the common basis from which related words in several languages can be derived by linguistic processes
- the set of values that give a true statement when substituted into an equation
- (linguistics) the form of a word after all affixes are removed
- the embedded part of a bodily structure such as a tooth, nail, or hair
- someone from whom you are descended (but usually more remote than a grandparent)
verb
- To fix firmly; to establish.
- (by extension) To seek favour or advancement by low arts or grovelling servility; to fawn.
- To grow roots; to enter the earth, as roots; to take root and begin to grow.
- (intransitive, with "for" or "on", US) To cheer (on); to show support (for) and hope for the success of. (See root for.)
- (transitive) To root out; to abolish.
- (intransitive) To rummage; to search as if by digging in soil.
- (computing slang, transitive) To get root or privileged access on (a computer system or mobile phone), often through bypassing some security mechanism.
- (Australia, New Zealand, Ireland, vulgar, slang) To sexually penetrate.
- (intransitive) Of a baby: to turn the head and open the mouth in search of food.
- (ambitransitive) To turn up or dig with the snout.
- (equestrianism, of a horse) To tug or pull at the reins aggressively by driving the head downwards while wearing a bit.
- To prepare, oversee, or otherwise cause the rooting of cuttings.
- cheer for
- become settled or established and stable in one's residence or life style
- come into existence, originate
- cause to take roots
- take root and begin to grow
- plant by the roots
- dig with the snout
noun
name
noun
- (linear algebra) The sum of the diagonal elements of a square matrix.
- (engineering) A connecting bar or rod, pivoted at each end to the end of another piece, for transmitting motion, especially from one plane to another; specifically, such a piece in an organ stop action to transmit motion from the trundle to the lever actuating the stop slider.
- An enquiry sent out for a missing article, such as a letter or an express package.
- A mark left as a sign of passage of a person or animal.
- An act of tracing.
- (meteorology) A small amount of rain, not enough to be measured.
- (semiotics) A signifier approximated in the absence of stable signified.
- A very small amount, often residual, of some substance or material.
- An informal road or prominent path in an arid area.
- (programming) A sequence of instructions, including branches but not loops, that is executed for some input data.
- (electronics) A current-carrying conductive pathway on a printed circuit board.
- (fortification) The ground plan of a work or works.
- (grammar) An empty category occupying a position in the syntactic structure from which something has been moved, used to explain constructions such as wh-movement and the passive.
- (geometry) The intersection of a plane of projection, or an original plane, with a coordinate plane.
- One of two straps, chains, or ropes of a harness, extending from the collar or breastplate to a whippletree attached to a vehicle or thing to be drawn; a tug.
- a just detectable amount
- a visible mark (as a footprint) left by the passage of person or animal or vehicle
- either of two lines that connect a horse's harness to a wagon or other vehicle or to a whiffletree
- a drawing created by superimposing a semitransparent sheet of paper on the original image and copying on it the lines of the original image
- an indication that something has been present
- a suggestion of some quality
adj
verb
- (transitive) To draw or sketch lightly or with care.
- (computing, transitive) To follow the execution of the program by making it to stop after every instruction, or by making it print a message after every step.
- (transitive) To follow the trail of.
- To follow the history of.
- (transitive) To copy onto a sheet of paper superimposed over the original, by drawing over its lines.
- make a mark or lines on a surface
- pursue or chase relentlessly
- follow, discover, or ascertain the course of development of something
- make one's course or travel along a path; travel or pass over, around, or along
- copy by following the lines of the original drawing on a transparent sheet placed upon it; make a tracing of
- read with difficulty
- to go back over again
- discover traces of
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adj
- (linear algebra, of matrix) Having no inverse.
- (linear algebra, of transformation) Having the property that the matrix of coefficients of the new variables has a determinant equal to zero.
- Being the only one of the kind; unique.
- Being only one of a larger population; single, individual.
- (set theory, of a cardinal number) Not equal to its own cofinality.
- Distinguished by superiority: peerless, unmatched, eminent, exceptional, extraordinary.
- (chiefly law) Each; individual.
- (grammar) Referring to only one thing or person.
- Out of the ordinary; curious.
- unusual or striking
- the single one of its kind
- being a single and separate person or thing
- beyond or deviating from the usual or expected
- grammatical number category referring to a single item or unit
- composed of one member, set, or kind
noun
adj
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
- (linear algebra, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
- (module theory, of a module) In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
- (representation theory, of a linear representation of a group or algebra) Being a direct sum of simple representations (also known as irreducible representations).
- (ring theory, of an algebra or ring) Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
- (category theory, most generally, of an abelian category) Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
- (Lie theory, of a Lie algebra) Being a direct sum of simple Lie algebras.
- (group theory, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial.
- (of a ring, somewhat proscribed) Semiprimitive: having trivial Jacobson radical.
adj
- (linear algebra) Said of a real, square matrix: that the product of it with a column vector on its right side and the transpose of that column vector on its left side is greater or equal to zero, only equaling zero if the vector itself is zero.
- (linear algebra) Said of a quadratic form: that the application of it to a tuple is greater or equal to zero, only equaling zero if the tuple itself is zero.
adj
noun
- A level or rank in an organization, profession, or society.
- (military) A formation of troops, ships, aircraft, etc., in diagonal parallel rows.
- (cycling) A line of riders seeking maximum drafting in a crosswind, resulting in a diagonal line across the road.
- a diffraction grating consisting of a pile of plates of equal thickness arranged stepwise with a constant offset
- status in a society or organization
- a body of troops arranged in a line
verb
adj
- (algebra, by extension, of two or more polynomials) Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).
- (number theory, of a positive integer) Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.
- (number theory, of two or more positive integers) Having no positive integer factors in common, aside from 1.
- (ring theory, by extension) (of two or more ideals of a ring) Whose sum is the whole ring; (of two or more elements of a ring) generating the whole ring.
adj
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example