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32 relations: Basis (linear algebra), Bijection, Binary relation, Category theory, Codomain, Completely multiplicative function, Domain of a function, Endomorphism, Equality (mathematics), Equation, Function (mathematics), Function composition, Identity element, Identity matrix, Inclusion map, Injective function, Integer, Isometry, Linear map, Mathematics, Metric space, Monoid, Morphism, Number theory, Set (mathematics), Set theory, Surjective function, Symmetry, Symmetry group, Topological space, Uniqueness quantification, Vector space.
Basis (linear algebra)
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Codomain
In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.
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Completely multiplicative function
In number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Endomorphism
In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself.
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Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
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Equation
In mathematics, an equation is a statement of an equality containing one or more variables.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Identity element
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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Inclusion map
In mathematics, if A is a subset of B, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \iota that sends each element, x, of A to x, treated as an element of B: A "hooked arrow" is sometimes used in place of the function arrow above to denote an inclusion map; thus: \iota: A\hookrightarrow B. (On the other hand, this notation is sometimes reserved for embeddings.) This and other analogous injective functions from substructures are sometimes called natural injections.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
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Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Monoid
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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Symmetry group
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Uniqueness quantification
In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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F(x)=x, Identity equation, Identity map, Identity mapping, Identity operation, Identity operator, Identity symmetry operator, Identity transformation.
References
[1] https://en.wikipedia.org/wiki/Identity_function
