English words for 'A nonzero blade of any grade associated with a linear function.'
Closest matches for "A nonzero blade of any grade associated with a linear function." are ranked by semantic fit across dictionary definitions.
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adj
- Of a pair of vectors: having a zero inner product; perpendicular.
- Of a square matrix: such that its transpose is equal to its inverse.
- (statistics) Statistically independent, with reference to variates.
- Of a linear transformation: preserving its angles.
- (geometry) Of two objects, at right angles; perpendicular to each other.
- Of a pair of elements in an ortholattice: each less than or equal to the orthocomplement of the other.
- (software engineering) Of two or more aspects of a problem, able to be treated separately; of a design, exhibiting consistency and composability.
- Of two or more problems or subjects, independent of or irrelevant to each other.
- Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal.
- having a set of mutually perpendicular axes; meeting at right angles
- not pertinent to the matter under consideration
- statistically unrelated
noun
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
- (algebraic geometry) Describing a curve the equation of which is nonic.
- Describing a type of beer glass used in British public houses; in the form of a truncated cone with a bulge around outside, just below the rim.
- (mathematics) Describing a polynomial that has 9 as the highest exponent of its terms.
adj
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (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)
- 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;.
- (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
noun
- (nonstandard) A circumflex ⟨ ˆ ⟩.
- (nonstandard) A háček ⟨ ˇ ⟩.
- An exponentiation symbol or operator ⟨＾⟩.
- (user interface) An indicator, often a blinking line or bar and usually called a cursor, indicating where the next insertion or other edit will take place.
- A mark ⟨ ‸ ⟩ used by writers and proofreaders to indicate that something is to be inserted at that point.
- a mark used by an author or editor to indicate where something is to be inserted into a text
noun
- (mathematics) A gradian.
- (Canada, education) A student of a particular grade (used with the grade level).
- (systematics) A taxon united by a level of morphological or physiological complexity that is not a clade.
- A rating.
- (Canada, US, Philippines, education) A level of primary and secondary education.
- (medicine) The degree of malignity of a tumor expressed on a scale.
- A slope (up or down) of a roadway or other passage
- (geometry) In a linear system of divisors on an n-dimensional variety, the number of free intersection points of n generic divisors.
- A degree or level of something; a position within a scale; a degree of quality.
- An area that has been flattened by a grader (construction machine).
- The level of the ground.
- A harsh scraping or cutting; a grating.
- (linguistics) Degree (any of the three stages (positive, comparative, superlative) in the comparison of an adjective or an adverb).
- (Philippines, ophthalmology) An eyeglass prescription.
- (chiefly Canada, US, Philippines) Performance on a test or other evaluation(s), expressed by a number, letter, or other symbol; a score.
- a position on a scale of intensity or amount or quality
- a variety of cattle produced by crossbreeding with a superior breed
- a number or letter indicating quality (especially of a student's performance)
- a relative position or degree of value in a graded group
- the gradient of a slope or road or other surface
- a degree of ablaut
- the height of the ground on which something stands
- one-hundredth of a right angle
- a body of students who are taught together
verb
- (linguistics) To describe, modify or inflect so as to classify as to degree.
- (sewing) To remove or trim part of a seam allowance from a finished seam so as to reduce bulk and make the finished piece more even when turned right side out.
- (chiefly Canada, US) To assign scores to the components of an academic test, or to overall academic performance.
- (intransitive) To pass imperceptibly from one grade into another.
- To organize in grades.
- To flatten, level, or smooth a large surface, especially with a grader.
- To apply classifying labels to data (typically by a manual rather than automatic process).
- (patternmaking) To increase or decrease the dimensions of a garment pattern from the initial base size in such a way that the overall proportions of the silhouette are maintained across all sizes.
- assign a grade or rank to, according to one's evaluation
- determine the grade of or assign a grade to
- assign a rank or rating to
- level to the right gradient
verb
- (transitive) To grade on a curve (bell curve of a normal distribution).
- (transitive) To bend; to crook.
- (intransitive) To bend or turn gradually from a given direction.
- (transitive) To cause to swerve from a straight course.
- (transitive, slang) To reject, to turn down romantic advances.
- extend in curves and turns
- form an arch or curve
- bend or cause to bend
- form a curl, curve, or kink
- turn sharply; change direction abruptly
noun
- (informal, usually in the plural) The attractive shape of a woman's body.
- (algebraic geometry) An algebraic curve; a polynomial relation of the planar coordinates.
- (analytic geometry) A continuous map from a one-dimensional space to a multidimensional space.
- (topology) A one-dimensional continuum.
- (geometry) A one-dimensional figure of non-zero length; the graph of a continuous map from a one-dimensional space.
- A gentle bend, such as in a road.
- A simple figure containing no straight portions and no angles; a curved line.
- (nonstandard, by extension) A grading system where all raw scores are raised by a set amount of points.
- A grading system based on the scale of performance of a group used to normalize a right-skewed grade distribution (with more lower scores) into a bell curve, so that more can receive higher grades, regardless of their actual knowledge of the subject.
- a pitch of a baseball that is thrown with spin so that its path curves as it approaches the batter
- curved segment (of a road or river or railroad track etc.)
- a line on a graph representing data
- the trace of a point whose direction of motion changes
- the property possessed by the curving of a line or surface
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
adj
- of a function or curve; extending without break or irregularity
- continuing in time or space without interruption
- Without intervening space; continued.
- (grammar) Expressing an ongoing action or state.
- (mathematics, more generally, of a function between two topological spaces) Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).
- (botany) Not deviating or varying from uniformity; not interrupted; not joined or articulated.
- Without stopping; without a break, cessation, or interruption.
- (mathematical analysis, of a function) Such that, for every x in the domain, for each small open interval D about f(x), there's an interval containing x whose image is in D.
adj
noun
- (mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.
- (mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
- a function of two variables i and j that equals 1 when i=j and equals 0 otherwise
adj
- (linear algebra, of matrix) Having no inverse.
- 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.
- (linear algebra, of transformation) Having the property that the matrix of coefficients of the new variables has a determinant equal to zero.
- (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
- (mathematics) Of a function: that is always nonincreasing or nondecreasing on an interval.
- (of speech or a sound) Having a single unvaried pitch.
- (printing) Synonym of monochrome.
- sounded or spoken in a tone unvarying in pitch
- of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value
noun
verb
noun
- (mathematics) A ring with no zero divisors; that is, in which no product of nonzero elements is zero.
- (geology) An area of more or less uniform mineralization.
- A group of related items, topics, or subjects.
- (data processing) A form of technical metadata that represent the type of a data item, its characteristics, name, and usage.
- (physics) A small region of a magnetic material with a consistent magnetization direction.
- A geographic area owned or controlled by a single person or organization.
- (taxonomy) The highest rank in the classification of organisms, above kingdom; in the three-domain system, one of the taxa Bacteria, Archaea, or Eukaryota.
- (mathematics, topology, mathematical analysis) An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.
- (more generally, of a binary relation R between A and B) The set A; The subset of A consisting of elements a of A such that there exists an element b in B with (a,b) in R.
- A field or sphere of activity, influence or expertise.
- (computing) The collection of computers identified by a domain's domain names.
- (mathematics, set theory) The set of input (argument) values for which a function is defined.
- (computing, Internet) Any DNS domain name, particularly one which has been delegated and has become representative of the delegated domain name and its subdomains.
- (biochemistry) A folded section of a protein molecule that has a discrete function; the equivalent section of a chromosome.
- (computing) Such a region used as a data storage element in a bubble memory.
- (computing, Internet) A collection of DNS or DNS-like domain names consisting of a delegated domain name and all its subdomains.
- (computing) A collection of information having to do with a domain, the computers named in the domain, and the network on which the computers named in the domain reside.
- the content of a particular field of knowledge
- territory over which rule or control is exercised
- (mathematics) the set of values of the independent variable for which a function is defined
- a particular environment or walk of life
- people in general; especially a distinctive group of people with some shared interest
noun
- a mathematical function whose graph (in Cartesian coordinates with uniform scales) is a line in the plane.
- (mathematics) Any function whose value on the sum of two elements is the sum of the values of the function on the two elements and whose value on the product of a scalar times an element is the scalar times the value of the function on the element: f(ax+by)=af(x)+bf(y)
- (mathematics) Any function whose graph is a straight line: f(x)=ax+b
noun
- a straight line that is the limiting value of a curve; can be considered as tangent at infinity
- (mathematical analysis) A straight line which a curve approaches arbitrarily closely as it goes to infinity. The limit of the curve; its tangent "at infinity".
- (by extension, figuratively) Anything which comes near to but never meets something else.
verb
adj
noun
noun
adj
- (mathematics) Of or pertaining to a broad field of mathematics that originates from the problem of calculating arc lengths of an ellipse.
- (botany, of leaves) Oval, with a short or no point.
- (linguistics) Of, or showing ellipsis; having a word or words omitted; elliptical.
- (geometry) Of or pertaining to an ellipse.
- (mathematics, in combination, of certain functions, equations and operators) That has coefficients satisfying a condition analogous to the condition for the general equation for a conic section to be of an ellipse.
- (of a leaf shape) in the form of an ellipse
- rounded like an egg
- characterized by extreme economy of expression or omission of superfluous elements
adj
- (geometry) Of a curve: having two infinite branches with a common asymptote, and a leaf-shaped loop.
- Of a leaf: having a (certain number of) leaflets.
- (geology) Synonym of foliated (“of a rock: having a structure of thin layers”).
- Shaped like or otherwise resembling a leaf; leaflike.
- Of or relating to leaves.
- Of a plant: having leaves.
- ornamented with foliage or foils
- (especially of metamorphic rock) having thin leaflike layers or strata
- (often used as a combining form) having or resembling a leaf or having a specified kind or number of leaves
noun
verb
- To add numbers to (a folio or leaf, or all the folios or leaves, of a book); also, to add numbers to the folios or leaves of (a book); to folio, to page, to paginate.
- (botany) Of a plant: to produce leaves.
- (architecture) To decorate (an architectural feature, as an arch or window) with foils (“small arcs in the traceries of arches, windows, etc.”).
- To split into layers or leaves.
- To spread (glass) with a thin coat of mercury and tin, or other substances forming a foil, to create a mirror; to foil, to silver.
- hammer into thin flat foils
- coat or back with metal foil
- decorate with leaves
- grow leaves
- number the pages of a book or manuscript
noun
- (nonstandard) A circumflex ⟨ ˆ ⟩.
- (nonstandard) A háček ⟨ ˇ ⟩.
- An exponentiation symbol or operator ⟨＾⟩.
- (user interface) An indicator, often a blinking line or bar and usually called a cursor, indicating where the next insertion or other edit will take place.
- A mark ⟨ ‸ ⟩ used by writers and proofreaders to indicate that something is to be inserted at that point.
- a mark used by an author or editor to indicate where something is to be inserted into a text
noun
- (mathematics) A gradian.
- (Canada, education) A student of a particular grade (used with the grade level).
- (systematics) A taxon united by a level of morphological or physiological complexity that is not a clade.
- A rating.
- (Canada, US, Philippines, education) A level of primary and secondary education.
- (medicine) The degree of malignity of a tumor expressed on a scale.
- A slope (up or down) of a roadway or other passage
- (geometry) In a linear system of divisors on an n-dimensional variety, the number of free intersection points of n generic divisors.
- A degree or level of something; a position within a scale; a degree of quality.
- An area that has been flattened by a grader (construction machine).
- The level of the ground.
- A harsh scraping or cutting; a grating.
- (linguistics) Degree (any of the three stages (positive, comparative, superlative) in the comparison of an adjective or an adverb).
- (Philippines, ophthalmology) An eyeglass prescription.
- (chiefly Canada, US, Philippines) Performance on a test or other evaluation(s), expressed by a number, letter, or other symbol; a score.
- a position on a scale of intensity or amount or quality
- a variety of cattle produced by crossbreeding with a superior breed
- a number or letter indicating quality (especially of a student's performance)
- a relative position or degree of value in a graded group
- the gradient of a slope or road or other surface
- a degree of ablaut
- the height of the ground on which something stands
- one-hundredth of a right angle
- a body of students who are taught together
verb
- (linguistics) To describe, modify or inflect so as to classify as to degree.
- (sewing) To remove or trim part of a seam allowance from a finished seam so as to reduce bulk and make the finished piece more even when turned right side out.
- (chiefly Canada, US) To assign scores to the components of an academic test, or to overall academic performance.
- (intransitive) To pass imperceptibly from one grade into another.
- To organize in grades.
- To flatten, level, or smooth a large surface, especially with a grader.
- To apply classifying labels to data (typically by a manual rather than automatic process).
- (patternmaking) To increase or decrease the dimensions of a garment pattern from the initial base size in such a way that the overall proportions of the silhouette are maintained across all sizes.
- assign a grade or rank to, according to one's evaluation
- determine the grade of or assign a grade to
- assign a rank or rating to
- level to the right gradient
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
- (mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.
- (mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
- a function of two variables i and j that equals 1 when i=j and equals 0 otherwise
noun
- (mathematics) A ring with no zero divisors; that is, in which no product of nonzero elements is zero.
- (geology) An area of more or less uniform mineralization.
- A group of related items, topics, or subjects.
- (data processing) A form of technical metadata that represent the type of a data item, its characteristics, name, and usage.
- (physics) A small region of a magnetic material with a consistent magnetization direction.
- A geographic area owned or controlled by a single person or organization.
- (taxonomy) The highest rank in the classification of organisms, above kingdom; in the three-domain system, one of the taxa Bacteria, Archaea, or Eukaryota.
- (mathematics, topology, mathematical analysis) An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.
- (more generally, of a binary relation R between A and B) The set A; The subset of A consisting of elements a of A such that there exists an element b in B with (a,b) in R.
- A field or sphere of activity, influence or expertise.
- (computing) The collection of computers identified by a domain's domain names.
- (mathematics, set theory) The set of input (argument) values for which a function is defined.
- (computing, Internet) Any DNS domain name, particularly one which has been delegated and has become representative of the delegated domain name and its subdomains.
- (biochemistry) A folded section of a protein molecule that has a discrete function; the equivalent section of a chromosome.
- (computing) Such a region used as a data storage element in a bubble memory.
- (computing, Internet) A collection of DNS or DNS-like domain names consisting of a delegated domain name and all its subdomains.
- (computing) A collection of information having to do with a domain, the computers named in the domain, and the network on which the computers named in the domain reside.
- the content of a particular field of knowledge
- territory over which rule or control is exercised
- (mathematics) the set of values of the independent variable for which a function is defined
- a particular environment or walk of life
- people in general; especially a distinctive group of people with some shared interest
noun
- a mathematical function whose graph (in Cartesian coordinates with uniform scales) is a line in the plane.
- (mathematics) Any function whose value on the sum of two elements is the sum of the values of the function on the two elements and whose value on the product of a scalar times an element is the scalar times the value of the function on the element: f(ax+by)=af(x)+bf(y)
- (mathematics) Any function whose graph is a straight line: f(x)=ax+b
noun
- a straight line that is the limiting value of a curve; can be considered as tangent at infinity
- (mathematical analysis) A straight line which a curve approaches arbitrarily closely as it goes to infinity. The limit of the curve; its tangent "at infinity".
- (by extension, figuratively) Anything which comes near to but never meets something else.
verb
noun
adj
- (mathematics) Of or pertaining to a broad field of mathematics that originates from the problem of calculating arc lengths of an ellipse.
- (botany, of leaves) Oval, with a short or no point.
- (linguistics) Of, or showing ellipsis; having a word or words omitted; elliptical.
- (geometry) Of or pertaining to an ellipse.
- (mathematics, in combination, of certain functions, equations and operators) That has coefficients satisfying a condition analogous to the condition for the general equation for a conic section to be of an ellipse.
- (of a leaf shape) in the form of an ellipse
- rounded like an egg
- characterized by extreme economy of expression or omission of superfluous elements
verb
- (transitive) To grade on a curve (bell curve of a normal distribution).
- (transitive) To bend; to crook.
- (intransitive) To bend or turn gradually from a given direction.
- (transitive) To cause to swerve from a straight course.
- (transitive, slang) To reject, to turn down romantic advances.
- extend in curves and turns
- form an arch or curve
- bend or cause to bend
- form a curl, curve, or kink
- turn sharply; change direction abruptly
noun
- (informal, usually in the plural) The attractive shape of a woman's body.
- (algebraic geometry) An algebraic curve; a polynomial relation of the planar coordinates.
- (analytic geometry) A continuous map from a one-dimensional space to a multidimensional space.
- (topology) A one-dimensional continuum.
- (geometry) A one-dimensional figure of non-zero length; the graph of a continuous map from a one-dimensional space.
- A gentle bend, such as in a road.
- A simple figure containing no straight portions and no angles; a curved line.
- (nonstandard, by extension) A grading system where all raw scores are raised by a set amount of points.
- A grading system based on the scale of performance of a group used to normalize a right-skewed grade distribution (with more lower scores) into a bell curve, so that more can receive higher grades, regardless of their actual knowledge of the subject.
- a pitch of a baseball that is thrown with spin so that its path curves as it approaches the batter
- curved segment (of a road or river or railroad track etc.)
- a line on a graph representing data
- the trace of a point whose direction of motion changes
- the property possessed by the curving of a line or surface
adj
- Of a pair of vectors: having a zero inner product; perpendicular.
- Of a square matrix: such that its transpose is equal to its inverse.
- (statistics) Statistically independent, with reference to variates.
- Of a linear transformation: preserving its angles.
- (geometry) Of two objects, at right angles; perpendicular to each other.
- Of a pair of elements in an ortholattice: each less than or equal to the orthocomplement of the other.
- (software engineering) Of two or more aspects of a problem, able to be treated separately; of a design, exhibiting consistency and composability.
- Of two or more problems or subjects, independent of or irrelevant to each other.
- Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal.
- having a set of mutually perpendicular axes; meeting at right angles
- not pertinent to the matter under consideration
- statistically unrelated
noun
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
- (algebraic geometry) Describing a curve the equation of which is nonic.
- Describing a type of beer glass used in British public houses; in the form of a truncated cone with a bulge around outside, just below the rim.
- (mathematics) Describing a polynomial that has 9 as the highest exponent of its terms.
adj
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (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)
- 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;.
- (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
- of a function or curve; extending without break or irregularity
- continuing in time or space without interruption
- Without intervening space; continued.
- (grammar) Expressing an ongoing action or state.
- (mathematics, more generally, of a function between two topological spaces) Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).
- (botany) Not deviating or varying from uniformity; not interrupted; not joined or articulated.
- Without stopping; without a break, cessation, or interruption.
- (mathematical analysis, of a function) Such that, for every x in the domain, for each small open interval D about f(x), there's an interval containing x whose image is in D.
adj
adj
- (linear algebra, of matrix) Having no inverse.
- 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.
- (linear algebra, of transformation) Having the property that the matrix of coefficients of the new variables has a determinant equal to zero.
- (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
- (mathematics) Of a function: that is always nonincreasing or nondecreasing on an interval.
- (of speech or a sound) Having a single unvaried pitch.
- (printing) Synonym of monochrome.
- sounded or spoken in a tone unvarying in pitch
- of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value
noun
verb
adj
noun
adj
- (geometry) Of a curve: having two infinite branches with a common asymptote, and a leaf-shaped loop.
- Of a leaf: having a (certain number of) leaflets.
- (geology) Synonym of foliated (“of a rock: having a structure of thin layers”).
- Shaped like or otherwise resembling a leaf; leaflike.
- Of or relating to leaves.
- Of a plant: having leaves.
- ornamented with foliage or foils
- (especially of metamorphic rock) having thin leaflike layers or strata
- (often used as a combining form) having or resembling a leaf or having a specified kind or number of leaves
noun
verb
- To add numbers to (a folio or leaf, or all the folios or leaves, of a book); also, to add numbers to the folios or leaves of (a book); to folio, to page, to paginate.
- (botany) Of a plant: to produce leaves.
- (architecture) To decorate (an architectural feature, as an arch or window) with foils (“small arcs in the traceries of arches, windows, etc.”).
- To split into layers or leaves.
- To spread (glass) with a thin coat of mercury and tin, or other substances forming a foil, to create a mirror; to foil, to silver.
- hammer into thin flat foils
- coat or back with metal foil
- decorate with leaves
- grow leaves
- number the pages of a book or manuscript