Matrix equivalence is an equivalence relation on the space of rectangular matrices. For two rectangular matrices of the same size, their equivalence can...

(mathematics) Equivalence relation Equivalence class Equivalence of categories, in category theory Equivalent infinitesimal Identity Matrix equivalence in linear...

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

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...

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

such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

reversible, row equivalence is an equivalence relation. It is commonly denoted by a tilde (~). There is a similar notion of column equivalence, defined by...

centralized systems with only additive uncertainty is the certainty equivalence property: that the optimal control solution in this case is the same...

theory. To see the equivalence, notice that if X is a left R-module then Xn is an Mn(R)-module where the module structure is given by matrix multiplication...

q ) {\displaystyle {\begin{matrix}p\nleftrightarrow q&=&(p\lor q)\land (\lnot p\lor \lnot q)\end{matrix}}} This equivalence can be established by applying...

columns, or by interchanging rows or columns. Up to equivalence, there is a unique Hadamard matrix of orders 1, 2, 4, 8, and 12. There are 5 inequivalent...

_{a'}=S\gamma _{a}S^{-1},} where S is a non-singular matrix. The sets γa′ and γa belong to the same equivalence class. Developed by Ettore Majorana, this Clifford...

algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;...

directly minimise the fill-in) by applying permutations to the matrix, or other such equivalence or similarity transformations. The Cuthill–McKee algorithm...

convergence is usually shown via the Lax equivalence theorem. Stability in this context means that a matrix norm of the matrix used in the iteration is at most...

other. Topological conjugacy, and related-but-distinct § Topological equivalence of flows, are important in the study of iterated functions and more generally...

recovered within the MHV Lagrangian framework via evasions of the S-matrix equivalence theorem. An alternative approach to the MHV Lagrangian recovers the...

begin with zero. More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

implementations of the Access Control Matrix, this view has been criticized as drawing a misleading equivalence between systems that does not take into...

A^{+}} ⁠ of a matrix ⁠ A {\displaystyle A} ⁠, often called the pseudoinverse, is the most widely known generalization of the inverse matrix. It was independently...

abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set...

pp. 556–562. C. Ding, X. He, H.D. Simon (2005). "On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering". Proc. SIAM Int'l Conf...

automorphic equivalence, and regular equivalence. There is a hierarchy of the three equivalence concepts: any set of structural equivalences are also automorphic...

orthogonal matrix transformations have the same trace: the trace is a class function. This matrix transformation is clearly an equivalence relation, that...

complex matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with...

defined as their dot product. So the equivalence of the two definitions of the dot product is a part of the equivalence of the classical and the modern formulations...

Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually...

probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled...