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...

} If A is an m × n matrix, then AT is an n × m matrix. A square matrix whose transpose is equal to itself is called a symmetric matrix; that is, A is...

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...

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...

invertible matrix (non-singular, non-degenarate or regular) is a square matrix that has an inverse. In other words, if some other matrix is multiplied...

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 {m}} -by-...

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...

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...

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

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...

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

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...

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...

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

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...

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}} ,...

In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots...

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...

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...

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...

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...

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...

A Stieltjes matrix is necessarily an M-matrix. Every n×n Stieltjes matrix is invertible to a nonsingular symmetric nonnegative matrix, though the converse...

m-by-n matrices A and B are called equivalent if B = Q − 1 A P {\displaystyle B=Q^{-1}AP} for some invertible n-by-n matrix P and some invertible m-by-m...

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

In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...

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

In-place matrix transposition, also called in-situ matrix transposition, is the problem of transposing an N×M matrix in-place in computer memory, ideally...

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...

nonnegative matrix is nonnegative. The inverse of any non-singular M-matrix [clarification needed] is a non-negative matrix. If the non-singular M-matrix is also...