especially linear algebra, an M-matrix is a matrix whose off-diagonal entries are less than or equal to zero (i.e., it is a Z-matrix) and whose eigenvalues have...

In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices...

\right]_{ji}.} If A is an m × n matrix, then AT is an n × m matrix. In the case of square matrices, AT may also denote the Tth power of the matrix A. For avoiding...

symmetric matrix   M   {\displaystyle \ M\ } with real entries is positive-definite if the real number   x ⊤ M x   {\displaystyle \ \mathbf {x} ^{\top }M\mathbf...

columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number...

an invertible matrix is a square matrix which has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can...

integers. A matrix with m {\displaystyle {m}} rows and n {\displaystyle {n}} columns is called an m × n {\displaystyle {m\times n}} matrix, or m {\displaystyle...

mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over...

unoriented incidence matrix (or simply incidence matrix) of an undirected graph is a n × m {\displaystyle n\times m} matrix B, where n and m are the numbers...

Matrix-M is a vaccine adjuvant, a substance that is added to various vaccines to stimulate the immune response. It was patented in 2020 by Novavax and...

mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices...

transpose, of an m × n {\displaystyle m\times n} complex matrix A {\displaystyle \mathbf {A} } is an n × m {\displaystyle n\times m} matrix obtained by transposing...

In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various...

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...

theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a...

of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries c i j = ∑ k = 1 m a i...

The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. It is the first installment in the Matrix film series, starring...

square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the...

complex matrix A {\displaystyle A} is a factorization of the form A = U P {\displaystyle A=UP} , where U {\displaystyle U} is a unitary matrix and P {\displaystyle...

any ⁠ m × n {\displaystyle m\times n} ⁠ matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an m × n {\displaystyle...

rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...

Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an ( m + 1 ) × ( n...

matrices as input and produces a block matrix Standard matrix multiplication Given two vectors of size m × 1 {\displaystyle m\times 1} and n × 1 {\displaystyle...

and entries in the field K {\displaystyle K} . A matrix norm is a norm on K m × n {\displaystyle K^{m\times n}} . Norms are often expressed with double...

over R, and may be called a matrix algebra. In this setting, if M is a matrix and r is in R, then the matrix rM is the matrix M with each of its entries...

normal matrix M ∗ M ∈ C N × N {\displaystyle M^{*}M\in \mathbb {C} ^{N\times N}} or M M ∗ ∈ C M × M {\displaystyle MM^{*}\in \mathbb {C} ^{M\times M}} ,...

An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM, results...

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices...

mathematics, a Q-matrix is a square matrix whose associated linear complementarity problem LCP(M,q) has a solution for every vector q. M is a Q-matrix if there...