invertible matrix P over the same field such that PTAP = B where "T" denotes the matrix transpose. Matrix congruence is an equivalence relation. Matrix congruence...

defined by congruence conditions on the entries of a matrix group with integer entries Congruence of squares, in number theory, a congruence commonly used...

only if they satisfy certain trace equalities. Canonical forms Matrix congruence Matrix equivalence Jacobi rotation Beauregard, Raymond A.; Fraleigh, John...

In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple...

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

{\displaystyle {\begin{pmatrix}1&2\\0&3\\\end{pmatrix}}} Row equivalence Matrix congruence Hefferon, Jim. Linear Algebra (4th ed.). pp. 270–272. This article...

In number theory, a congruence of squares is a congruence commonly used in integer factorization algorithms. Given a positive integer n, Fermat's factorization...

small integers. The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain. It has been generalized to...

1063/1.1724294. Youla, D. C. (1961). "A normal form for a matrix under the unitary congruence group". Can. J. Math. 13: 694–704. doi:10.4153/CJM-1961-059-8...

semigroup congruence ~ induces congruence classes [a]~ = {x ∈ S | x ~ a} and the semigroup operation induces a binary operation ∘ on the congruence classes:...

complement Haynsworth inertia additivity formula Matrix equivalence Matrix congruence Matrix similarity Matrix consimilarity Row equivalence Elementary row...

matrices, P is invertible, and PT denotes the transpose of P; see Matrix Congruence and congruence in linear algebra. This disambiguation page lists articles...

In mathematics, Gauss congruence is a property held by certain sequences of integers, including the Lucas numbers and the divisor sum sequence. Sequences...

Discovery and Data Mining Confirmatory factor analysis Confusion matrix Congruence coefficient Connect (computer system) Consensus clustering Constrained...

Important subgroups of the modular group Γ, called congruence subgroups, are given by imposing congruence relations on the associated matrices. There is a...

congruence of squares; and the data processing phase, where it puts all the data it has collected into a matrix and solves it to obtain a congruence of...

Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant...

matrices, where the group operation is given by matrix multiplication (an orthogonal matrix is a real matrix whose inverse equals its transpose). The orthogonal...

exploits unevenness in how the cipher operates over equivalence classes (congruence classes) modulo n. The method was first suggested in 1999 by John Kelsey...

and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean...

real-valued n-by-n square matrices with the matrix-transpose as the involution. The map which sends a matrix to its transpose is an involution because the...

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed...

(2,3,7) triangle group, after quotienting by the center. The principal congruence subgroup defined by an ideal I ⊂ Z [ η ] {\displaystyle I\subset \mathbb...

isomorphism theorems can be generalized to the context of algebras and congruences. The isomorphism theorems were formulated in some generality for homomorphisms...

decomposition of an integer matrix m. Smith, Henry J. Stephen (1861). "On systems of linear indeterminate equations and congruences". Phil. Trans. R. Soc....

This congruence may generate the trivial n = 1 ⋅ n {\displaystyle \textstyle n=1\cdot n} ; in this case we try to find another suitable congruence. If...

Retrieved 2023-01-09. Jardine, Kevin. "Shield - a 3.7.42 tiling". Imperfect Congruence. Retrieved 2023-01-09. 3.7.42 as a unit facet in an irregular tiling....

R) with the discrete subgroup being the modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension...

fields (also known as Galois fields). The algorithm consists mainly of matrix reduction and polynomial GCD computations. It was invented by Elwyn Berlekamp...

H_{n}^{(2)}=\left[{\begin{matrix}n+1\\2\end{matrix}}\right]^{2}-2\left[{\begin{matrix}n+1\\1\end{matrix}}\right]\left[{\begin{matrix}n+1\\3\end{matrix}}\right]} ( n...