「(mathematics, functional analysis) A scalar-valued linear function on a vector space.」のEnglishの単語
上に「(mathematics, functional analysis) A scalar-valued linear function on a vector space.」に関連する単語が表示されています。詳しく知りたい単語にマウスを合わせると定義が表示されます。検索アイコンをクリックするとより適切な単語を見つけられます。ChatGPTのおかげで、全体的な結果が大幅に改善されました。
検索結果
noun
- (mathematics, functional analysis) A scalar-valued linear function on a vector space.
- (mathematics) A function that takes a function as its argument; more precisely, a function whose argument varies in a space of (real or complex valued) functions and whose value belongs to a monodimensional space.
- (computing) An object encapsulating a function pointer (or equivalent).
adj
- Optimized for all-around physiological benefit.
- Useful; serving a purpose, fulfilling a function.
- (computing theory) Having semantics defined purely in terms of mathematical functions, without side-effects.
- (mathematics) Of or relating to a function or functions.
- Of or relating to one's role or office; official.
- Only for functional purposes, notably in architecture.
- In good working order.
- (physiology, psychology) Characterizing functioning in environment, being symptoms that do not presuppose alteration of organic structure.
- designed for or adapted to a function or use
- involving or affecting function rather than physiology
- (of e.g. a machine) performing or capable of performing
- relating to or based on function especially as opposed to structure
- designed for or capable of a particular function or use
- fit or ready for use or service
noun
- (linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.
- A physical base or foundation.
- A starting point, base or foundation for an argument or hypothesis.
- (topology) A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.
- An underlying condition or circumstance.
- (accounting) Amount paid for an investment, including commissions and other expenses.
- A regular frequency.
- (agriculture, trading) The difference between the cash price a dealer pays to a farmer for his produce and an agreed reference price, which is usually the futures price at which the given crop is trading at a commodity exchange.
- the fundamental assumptions from which something is begun or developed or calculated or explained
- a relation that provides the foundation for something
- the most important or necessary part of something
noun
- (mathematics) Any member of a (generalized) vector space.
- (computer graphics, attributive) A graphical representation using outlines; vector graphics.
- (history) Forces, developments, phenomena, processes, systems, etc. which influence the trajectory of history (e.g. imperialism)
- (aviation) A chosen course or direction for motion, as of an aircraft.
- (programming) A kind of dynamically resizable array.
- (psychology) A recurring psychosocial issue that stimulates growth and development in the personality.
- (sociology) A person or entity that passes along an urban legend or other meme.
- (mathematics, computing) An ordered tuple, originally one representing a directed quantity, but by extension any one-dimensional matrix.
- (mathematics, physics) A directed quantity, one with both magnitude and direction; the signed difference between two points.
- (molecular biology) A DNA molecule used to carry genetic information from one organism into another.
- (computing, operating systems) A memory address containing the address of a code entry point, usually one which is part of a table and often one that is dereferenced and jumped to during the execution of an interrupt.
- a straight line segment whose length is magnitude and whose orientation in space is direction
- (genetics) a virus or other agent that is used to deliver DNA to a cell
- any agent (person or animal or microorganism) that carries and transmits a disease
- a variable quantity that can be resolved into components
verb
noun
- a generalization of the concept of a vector
- any of several muscles that cause an attached structure to become tense or firm
- (engineering, computing) A multidimensional array with (at least) two dimensions.
- (anatomy) A muscle that tightens or stretches a part, or renders it tense.
- (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array.
verb
adj
- (linear algebra) Being the space of all linear functionals of (some other space).
- (grammar) Pertaining to a grammatical number in certain languages that refers to two of something, such as a pair of shoes.
- Pertaining to two, pertaining to a pair of.
- (category theory) Being the dual of some other category; containing the same objects but with source and target reversed for all morphisms.
- (mathematics, physics) Exhibiting duality.
- Characterized by having two (usually equivalent) components.
- having more than one decidedly dissimilar aspects or qualities
- consisting of or involving two parts or components usually in pairs
- a grammatical number category referring to two items or units as opposed to one item (singular) or more than two items (plural)
noun
- (mathematics) Of a vector in an inner product space, the linear functional corresponding to taking the inner product with that vector. The set of all duals is a vector space called the dual space.
- (geometry) Of a regular polyhedron with V vertices and F faces, the regular polyhedron having F vertices and V faces.
- (wrestling) A head-to-head match or meet between two teams, such as two high schools or colleges.
- (grammar) The dual number.
- Of an item that is one of a pair, the other item in the pair.
verb
noun
- (mathematics, linear algebra) A sequence of subspaces of a vector space, beginning with the null space and ending with the vector space itself, such that each member of the sequence (until the last) is a proper subspace of the next.
- (Internet slang, ACG) An indication that a certain outcome or event is going to happen, deduced not logically or causally, but as a pattern in a piece of media. Chiefly used in video games and adjacent media, especially visual novels, it is typically described as being raised or set by the plot or words of a character.
- (computer science) In a command line interface, a command parameter requesting optional behavior or otherwise modifying the action of the command being invoked.
- (nautical, often used attributively) A signal flag.
- The design that could be placed on a flag, typically a rectangular graphic that is used to represent an entity (like a country, organisation or group of people) or an idea.
- Any of various plants with sword-shaped leaves, especially irises; specifically, Iris pseudacorus.
- (computer science) A variable or memory location that stores a Boolean true-or-false, yes-or-no value, typically either recording the fact that a certain event has occurred or requesting that a certain optional action take place.
- A group of feathers on the lower part of the legs of certain hawks, owls, etc.
- The bushy tail of a dog such as a setter.
- (aviation) A mechanical indicator that pops up to draw the pilot's attention to a problem or malfunction.
- (geology) Any hard, evenly stratified sandstone, which splits into layers suitable for flagstones.
- (British, uncountable) The game of capture the flag.
- A group of elongated wing feathers in certain hawks.
- A slab of stone; a flagstone, a flat piece of stone used for paving.
- (geometry) A sequence of faces of a given polytope, one of each dimension up to that of the polytope (formally, though in practice not always explicitly, including the null face and the polytope itself), such that each face in the sequence is part of the next-higher dimension face.
- (countable) A piece of cloth, often decorated with an emblem, used as a visual signal or symbol.
- The use of a flag, especially to indicate the start of a race or other event.
- (nautical) A flag flown by a ship to show the presence on board of the admiral; the admiral himself, or his flagship.
- (television) A dark piece of material that can be mounted on a stand to block or shape the light.
- (obsolete except in dialects) A slice of turf; a sod.
- (music) A hook attached to the stem of a written note that assigns its rhythmic value
- a conspicuously marked or shaped tail
- a listing printed in all issues of a newspaper or magazine (usually on the editorial page) that gives the name of the publication and the names of the editorial staff, etc.
- emblem usually consisting of a rectangular piece of cloth of distinctive design
- flagpole used to mark the position of the hole on a golf green
- a rectangular piece of fabric used as a signalling device
- stratified stone that splits into pieces suitable as paving stones
- plants with sword-shaped leaves and erect stalks bearing bright-colored flowers composed of three petals and three drooping sepals
verb
- (computing) To signal (an event).
- (transitive) To pave with flagstones.
- To fail, such as a class or an exam.
- (often with up) To note, mark or point out for attention.
- To mark with a flag, especially to indicate the importance of something.
- (sports) To penalize for an infraction.
- (chess, intransitive) To lose on time, especially in a blitz game; when using a traditional analog chess clock, a flag would fall when time expired.
- To furnish or deck out with flags.
- (computing) To set a program variable to true.
- To convey (a message) by means of flag signals.
- (firearms) To point the muzzle of a firearm at a person or object one does not intend to fire on.
- (biology) In female canids, to signal mating readiness by moving the tail aside to expose the vulva.
- (chess, transitive) To defeat (an opponent) on time, especially in a blitz game.
- (often with down) To signal to, especially to stop a passing vehicle etc.
- To enervate; to exhaust the vigour or elasticity of.
- (intransitive) To weaken, become feeble.
- To hang loose without stiffness; to bend down, as flexible bodies; to be loose, yielding, limp.
- To let droop; to suffer to fall, or let fall, into feebleness.
- To decoy (game) by waving a flag, handkerchief, etc. to arouse the animal's curiosity.
- communicate or signal with a flag
- droop, sink, or settle from or as if from pressure or loss of tautness
- provide with a flag
- decorate with flags
- become less intense
adj
noun
adj
- (of a function between vector spaces) An additive, homogeneous mapping; that is, a function f:V→W is linear if it distributes over vector addition (f( mathbf v+ mathbf w)=f( mathbf v)+f( mathbf w)) and respects scalar multiplication (f(c mathbf v)=cf( mathbf v)). If V and W are vector spaces over a field K, f may also be called a K-linear map. See also linear map on Wikipedia.Wikipedia
- (botany, of leaves) Long and narrow, with nearly parallel sides.
- (media, of video and audio) Delivered or delivering on a fixed schedule, as opposed to on-demand.
- Of or relating to lines.
- (physics) A type of length measurement involving only one spatial dimension (as opposed to area or volume).
- Made, or designed to be used, in a step-by-step, sequential manner.
- Having the form of a line; straight or roughly straight; following a direct course.
- (of a function over a module) A module homomorphism; that is, a group homomorphism that commutes with scalar multiplication. See also Module homomorphism on Wikipedia.Wikipedia
- (of a polynomial) Having degree one; that is, being of the form a_1x_1+a_2x_2+⋯+a_nx_n+b, where each x_i is a variable. See also Linear polynomials on Wikipedia.Wikipedia
- (of a polynomial equation) Involving only linear polynomials. See also Linear equation on Wikipedia.Wikipedia
- measured lengthwise
- of or in or along or relating to a line; involving or having a single dimension
- (of a leaf shape) long and narrow
- of a circuit or device having an output that is proportional to the input
- designating or involving an equation whose terms are of the first degree
noun
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
- (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(
- (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.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- 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.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (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;.
- (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
noun
- (calculus) The operator which maps a function F=(F₁, ... Fₙ) from a n-dimensional vector space to itself to the function ∑ᵢ₌₁ⁿ(∂F_i)/(∂x_i).
- The process in which two or more populations accumulate genetic changes (mutations) through time.
- The state or degree of being divergent: of diverging.
- a difference between conflicting facts or claims or opinions
- an infinite series that has no limit
- a variation that deviates from the standard or norm
- the act of moving away in different direction from a common point
noun
- (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.
- (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, linear algebra) The set of eigenvalues of a matrix.
- 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
adj
- (mathematics, of a function of hyperreals) Both additive and homogeneous for hyperreal scalars.
- (dermatology) Having unusually pronounced creases marking the skin.
- (mathematics, curve fitting) Increasing exponentially or as a higher polynomial power.
- (mathematics, of groups) Displaying a generalization of sofic that applies to finite-dimensional Hilbert spaces.
- (mathematics, of a sequence) Converging very quickly to a limit so that the ratio of adjacent terms tends to zero.
noun
- (mathematics, functional analysis) A scalar-valued linear function on a vector space.
- (mathematics) A function that takes a function as its argument; more precisely, a function whose argument varies in a space of (real or complex valued) functions and whose value belongs to a monodimensional space.
- (computing) An object encapsulating a function pointer (or equivalent).
adj
- Optimized for all-around physiological benefit.
- Useful; serving a purpose, fulfilling a function.
- (computing theory) Having semantics defined purely in terms of mathematical functions, without side-effects.
- (mathematics) Of or relating to a function or functions.
- Of or relating to one's role or office; official.
- Only for functional purposes, notably in architecture.
- In good working order.
- (physiology, psychology) Characterizing functioning in environment, being symptoms that do not presuppose alteration of organic structure.
- designed for or adapted to a function or use
- involving or affecting function rather than physiology
- (of e.g. a machine) performing or capable of performing
- relating to or based on function especially as opposed to structure
- designed for or capable of a particular function or use
- fit or ready for use or service
noun
- (linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.
- A physical base or foundation.
- A starting point, base or foundation for an argument or hypothesis.
- (topology) A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.
- An underlying condition or circumstance.
- (accounting) Amount paid for an investment, including commissions and other expenses.
- A regular frequency.
- (agriculture, trading) The difference between the cash price a dealer pays to a farmer for his produce and an agreed reference price, which is usually the futures price at which the given crop is trading at a commodity exchange.
- the fundamental assumptions from which something is begun or developed or calculated or explained
- a relation that provides the foundation for something
- the most important or necessary part of something
noun
- (mathematics) Any member of a (generalized) vector space.
- (computer graphics, attributive) A graphical representation using outlines; vector graphics.
- (history) Forces, developments, phenomena, processes, systems, etc. which influence the trajectory of history (e.g. imperialism)
- (aviation) A chosen course or direction for motion, as of an aircraft.
- (programming) A kind of dynamically resizable array.
- (psychology) A recurring psychosocial issue that stimulates growth and development in the personality.
- (sociology) A person or entity that passes along an urban legend or other meme.
- (mathematics, computing) An ordered tuple, originally one representing a directed quantity, but by extension any one-dimensional matrix.
- (mathematics, physics) A directed quantity, one with both magnitude and direction; the signed difference between two points.
- (molecular biology) A DNA molecule used to carry genetic information from one organism into another.
- (computing, operating systems) A memory address containing the address of a code entry point, usually one which is part of a table and often one that is dereferenced and jumped to during the execution of an interrupt.
- a straight line segment whose length is magnitude and whose orientation in space is direction
- (genetics) a virus or other agent that is used to deliver DNA to a cell
- any agent (person or animal or microorganism) that carries and transmits a disease
- a variable quantity that can be resolved into components
verb
noun
- a generalization of the concept of a vector
- any of several muscles that cause an attached structure to become tense or firm
- (engineering, computing) A multidimensional array with (at least) two dimensions.
- (anatomy) A muscle that tightens or stretches a part, or renders it tense.
- (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array.
verb
noun
- (mathematics, linear algebra) A sequence of subspaces of a vector space, beginning with the null space and ending with the vector space itself, such that each member of the sequence (until the last) is a proper subspace of the next.
- (Internet slang, ACG) An indication that a certain outcome or event is going to happen, deduced not logically or causally, but as a pattern in a piece of media. Chiefly used in video games and adjacent media, especially visual novels, it is typically described as being raised or set by the plot or words of a character.
- (computer science) In a command line interface, a command parameter requesting optional behavior or otherwise modifying the action of the command being invoked.
- (nautical, often used attributively) A signal flag.
- The design that could be placed on a flag, typically a rectangular graphic that is used to represent an entity (like a country, organisation or group of people) or an idea.
- Any of various plants with sword-shaped leaves, especially irises; specifically, Iris pseudacorus.
- (computer science) A variable or memory location that stores a Boolean true-or-false, yes-or-no value, typically either recording the fact that a certain event has occurred or requesting that a certain optional action take place.
- A group of feathers on the lower part of the legs of certain hawks, owls, etc.
- The bushy tail of a dog such as a setter.
- (aviation) A mechanical indicator that pops up to draw the pilot's attention to a problem or malfunction.
- (geology) Any hard, evenly stratified sandstone, which splits into layers suitable for flagstones.
- (British, uncountable) The game of capture the flag.
- A group of elongated wing feathers in certain hawks.
- A slab of stone; a flagstone, a flat piece of stone used for paving.
- (geometry) A sequence of faces of a given polytope, one of each dimension up to that of the polytope (formally, though in practice not always explicitly, including the null face and the polytope itself), such that each face in the sequence is part of the next-higher dimension face.
- (countable) A piece of cloth, often decorated with an emblem, used as a visual signal or symbol.
- The use of a flag, especially to indicate the start of a race or other event.
- (nautical) A flag flown by a ship to show the presence on board of the admiral; the admiral himself, or his flagship.
- (television) A dark piece of material that can be mounted on a stand to block or shape the light.
- (obsolete except in dialects) A slice of turf; a sod.
- (music) A hook attached to the stem of a written note that assigns its rhythmic value
- a conspicuously marked or shaped tail
- a listing printed in all issues of a newspaper or magazine (usually on the editorial page) that gives the name of the publication and the names of the editorial staff, etc.
- emblem usually consisting of a rectangular piece of cloth of distinctive design
- flagpole used to mark the position of the hole on a golf green
- a rectangular piece of fabric used as a signalling device
- stratified stone that splits into pieces suitable as paving stones
- plants with sword-shaped leaves and erect stalks bearing bright-colored flowers composed of three petals and three drooping sepals
verb
- (computing) To signal (an event).
- (transitive) To pave with flagstones.
- To fail, such as a class or an exam.
- (often with up) To note, mark or point out for attention.
- To mark with a flag, especially to indicate the importance of something.
- (sports) To penalize for an infraction.
- (chess, intransitive) To lose on time, especially in a blitz game; when using a traditional analog chess clock, a flag would fall when time expired.
- To furnish or deck out with flags.
- (computing) To set a program variable to true.
- To convey (a message) by means of flag signals.
- (firearms) To point the muzzle of a firearm at a person or object one does not intend to fire on.
- (biology) In female canids, to signal mating readiness by moving the tail aside to expose the vulva.
- (chess, transitive) To defeat (an opponent) on time, especially in a blitz game.
- (often with down) To signal to, especially to stop a passing vehicle etc.
- To enervate; to exhaust the vigour or elasticity of.
- (intransitive) To weaken, become feeble.
- To hang loose without stiffness; to bend down, as flexible bodies; to be loose, yielding, limp.
- To let droop; to suffer to fall, or let fall, into feebleness.
- To decoy (game) by waving a flag, handkerchief, etc. to arouse the animal's curiosity.
- communicate or signal with a flag
- droop, sink, or settle from or as if from pressure or loss of tautness
- provide with a flag
- decorate with flags
- become less intense
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
- (calculus) The operator which maps a function F=(F₁, ... Fₙ) from a n-dimensional vector space to itself to the function ∑ᵢ₌₁ⁿ(∂F_i)/(∂x_i).
- The process in which two or more populations accumulate genetic changes (mutations) through time.
- The state or degree of being divergent: of diverging.
- a difference between conflicting facts or claims or opinions
- an infinite series that has no limit
- a variation that deviates from the standard or norm
- the act of moving away in different direction from a common point
noun
- (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.
- (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, linear algebra) The set of eigenvalues of a matrix.
- 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
adj
- (linear algebra) Being the space of all linear functionals of (some other space).
- (grammar) Pertaining to a grammatical number in certain languages that refers to two of something, such as a pair of shoes.
- Pertaining to two, pertaining to a pair of.
- (category theory) Being the dual of some other category; containing the same objects but with source and target reversed for all morphisms.
- (mathematics, physics) Exhibiting duality.
- Characterized by having two (usually equivalent) components.
- having more than one decidedly dissimilar aspects or qualities
- consisting of or involving two parts or components usually in pairs
- a grammatical number category referring to two items or units as opposed to one item (singular) or more than two items (plural)
noun
- (mathematics) Of a vector in an inner product space, the linear functional corresponding to taking the inner product with that vector. The set of all duals is a vector space called the dual space.
- (geometry) Of a regular polyhedron with V vertices and F faces, the regular polyhedron having F vertices and V faces.
- (wrestling) A head-to-head match or meet between two teams, such as two high schools or colleges.
- (grammar) The dual number.
- Of an item that is one of a pair, the other item in the pair.
verb
一致する単語が見つかりませんでした。より広い説明を試してください。
adj
- (linear algebra) Being the space of all linear functionals of (some other space).
- (grammar) Pertaining to a grammatical number in certain languages that refers to two of something, such as a pair of shoes.
- Pertaining to two, pertaining to a pair of.
- (category theory) Being the dual of some other category; containing the same objects but with source and target reversed for all morphisms.
- (mathematics, physics) Exhibiting duality.
- Characterized by having two (usually equivalent) components.
- having more than one decidedly dissimilar aspects or qualities
- consisting of or involving two parts or components usually in pairs
- a grammatical number category referring to two items or units as opposed to one item (singular) or more than two items (plural)
noun
- (mathematics) Of a vector in an inner product space, the linear functional corresponding to taking the inner product with that vector. The set of all duals is a vector space called the dual space.
- (geometry) Of a regular polyhedron with V vertices and F faces, the regular polyhedron having F vertices and V faces.
- (wrestling) A head-to-head match or meet between two teams, such as two high schools or colleges.
- (grammar) The dual number.
- Of an item that is one of a pair, the other item in the pair.
verb
adj
noun
adj
- (of a function between vector spaces) An additive, homogeneous mapping; that is, a function f:V→W is linear if it distributes over vector addition (f( mathbf v+ mathbf w)=f( mathbf v)+f( mathbf w)) and respects scalar multiplication (f(c mathbf v)=cf( mathbf v)). If V and W are vector spaces over a field K, f may also be called a K-linear map. See also linear map on Wikipedia.Wikipedia
- (botany, of leaves) Long and narrow, with nearly parallel sides.
- (media, of video and audio) Delivered or delivering on a fixed schedule, as opposed to on-demand.
- Of or relating to lines.
- (physics) A type of length measurement involving only one spatial dimension (as opposed to area or volume).
- Made, or designed to be used, in a step-by-step, sequential manner.
- Having the form of a line; straight or roughly straight; following a direct course.
- (of a function over a module) A module homomorphism; that is, a group homomorphism that commutes with scalar multiplication. See also Module homomorphism on Wikipedia.Wikipedia
- (of a polynomial) Having degree one; that is, being of the form a_1x_1+a_2x_2+⋯+a_nx_n+b, where each x_i is a variable. See also Linear polynomials on Wikipedia.Wikipedia
- (of a polynomial equation) Involving only linear polynomials. See also Linear equation on Wikipedia.Wikipedia
- measured lengthwise
- of or in or along or relating to a line; involving or having a single dimension
- (of a leaf shape) long and narrow
- of a circuit or device having an output that is proportional to the input
- designating or involving an equation whose terms are of the first degree
noun
adj
- (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(
- (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.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- 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.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (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;.
- (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
- (mathematics, of a function of hyperreals) Both additive and homogeneous for hyperreal scalars.
- (dermatology) Having unusually pronounced creases marking the skin.
- (mathematics, curve fitting) Increasing exponentially or as a higher polynomial power.
- (mathematics, of groups) Displaying a generalization of sofic that applies to finite-dimensional Hilbert spaces.
- (mathematics, of a sequence) Converging very quickly to a limit so that the ratio of adjacent terms tends to zero.