mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly...

In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

sum of permutations Enumerations of specific permutation classes Factorial Falling factorial Permutation matrix Generalized permutation matrix Inversion...

reflection matrix with θ = 90° generates a reflection about the line at 45° given by y = x and therefore exchanges x and y; it is a permutation matrix, with...

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 = [...

can be described in matrix form, with a mass matrix multiplying a generalized velocity to give the kinetic term, and a force matrix multiplying a displacement...

epsilon represents a collection of numbers; defined from the sign of a permutation of the natural numbers 1, 2, ..., n, for some positive integer n. It...

Generalizing the above to higher dimensions, the determinant of an n × n {\displaystyle n\times n} matrix is an expression involving permutations and...

The trace of a Hermitian matrix is real, because the elements on the diagonal are real. The trace of a permutation matrix is the number of fixed points...

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

method for determining whether a given permutation is even or odd is to construct the corresponding permutation matrix and compute its determinant. The value...

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...

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

{\displaystyle 1/p!} in § Properties of the generalized Kronecker delta below disappearing. In terms of the indices, the generalized Kronecker delta is defined as:...

a single-matrix SVD. The generalized singular value decomposition (GSVD) is a matrix decomposition on a pair of matrices which generalizes the singular...

diagonalizable. A matrix that is not diagonalizable is said to be defective. For defective matrices, the notion of eigenvectors generalizes to generalized eigenvectors...

}+\left[{\begin{matrix}n-1\\k-1\end{matrix}}\right]_{\alpha }+\delta _{n,0}\delta _{k,0}\,.} These generalized α-factorial coefficients then generate...

In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing...

first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to their number of cycles...

matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can...

ISBN 0-12-471252-5. McCullagh, P.; Nelder, J. A. (1989), "An outline of generalized linear models", Generalized Linear Models, Springer US, pp. 21–47, doi:10.1007/978-1-4899-3242-6_2...

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

least if B is a non-negative monomial matrix. In this simple case it will just correspond to a scaling and a permutation. More control over the non-uniqueness...

triangular, and P is a permutation matrix. Existence: An LUP decomposition exists for any square matrix A. When P is an identity matrix, the LUP decomposition...

the former context. A permutation matrix is an alternating sign matrix, and an alternating sign matrix is a permutation matrix if and only if no entry...

semistandard tableau for Q as well. The two-line array (or generalized permutation) wA corresponding to a matrix A is defined as w A = ( i 1 i 2 … i m j 1 j 2 …...

fact just a subgroup of a permutation group (up to isomorphism). The set of all bijective functions f: X → X (called permutations) forms a group with respect...

to generalize the cross product to higher dimensions. The cross product can be seen as one of the simplest Lie products, and is thus generalized by Lie...

In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth...