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...

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...

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

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...

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...

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

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

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

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...

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...

_{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...

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...

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

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...

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

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

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...

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...

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

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

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...

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...

symmetric matrix A is uniquely determined by the corresponding quadratic form. Under an equivalence C, the symmetric matrix A of φ and the symmetric matrix B...

dynamics are related by S {\displaystyle S} -matrix-preserving unitary transformations. The equivalence in field theories is more complicated because...

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