In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector...

integer factorization algorithms Matrix congruence, an equivalence relation between two matrices Congruence (manifolds), in the theory of smooth manifolds...

integer k such that a − b = k m. Congruence modulo m is a congruence relation, meaning that it is an equivalence relation that is compatible with the operations...

where "T" denotes the matrix transpose. Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of...

using a congruence relation. Quotient algebras are also called factor algebras. Here, the congruence relation must be an equivalence relation that is...

structure. In general, congruence relations play the role of kernels of homomorphisms, and the quotient of a structure by a congruence relation can be formed....

In number theory, the Eichler–Shimura congruence relation expresses the local L-function of a modular curve at a prime p in terms of the eigenvalues of...

(an element of the Euclidean group E(n)) with f(A) = B. Congruence is an equivalence relation. Two conic sections are congruent if their eccentricities...

whether a homomorphism is injective. In these cases, the kernel is a congruence relation. This article is a survey for some important types of kernels in...

when one may be moved to coincide with the other, and the equality/congruence relation is the isomorphism classes of isometries between shapes. Similarly...