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Rank–nullity theorem

The rank–nullity theorem is a theorem in linear algebra, which asserts that the dimension of the domain of a linear map is the sum of its rank (the dimension of its image) and its nullity (the dimensi

List of set identities and relations

This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It

Fundamental theorem of linear algebra

In mathematics, the fundamental theorem of linear algebra is a collection of statements regarding vector spaces and linear algebra, popularized by Gilbert Strang. The naming of these results is not un

Correspondence theorem

In group theory, the correspondence theorem (also the lattice theorem, and variously and ambiguously the third and fourth isomorphism theorem) states that if is a normal subgroup of a group , then the

Cokernel

The cokernel of a linear mapping of vector spaces f : X → Y is the quotient space Y / im(f) of the codomain of f by the image of f. The dimension of the cokernel is called the corank of f. Cokernels a

Isomorphism theorems

In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between quotients, homomorphisms, and

Kernel (algebra)

In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation is denoted multiplicatively, where the kernel is

Colour refinement algorithm

In graph theory and theoretical computer science, the colour refinement algorithm also known as the naive vertex classification, or the 1-dimensional version of the Weisfeiler-Leman algorithm, is a ro

Zassenhaus lemma

In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Zassenhaus, is a technical result on the lattice of subgroups of a group or the of a module, or more generally for any modular

Image (mathematics)

In mathematics, the image of a function is the set of all output values it may produce. More generally, evaluating a given function at each element of a given subset of its domain produces a set, call

Coimage

In algebra, the coimage of a homomorphism is the quotient of the domain by the kernel. The coimage is canonically isomorphic to the image by the first isomorphism theorem, when that theorem applies. M

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