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...

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

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

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 = [...

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

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...

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

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

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...

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...

^{n\times n}} be permutation matrices; and D ∈ R m × n {\displaystyle \mathbf {D} \in \mathbb {R} ^{m\times n}} an arbitrary matrix. The softmax function...

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

The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms...

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...

set of all m-permutations of the n-set {1,2,...,n}. Ryser's computational result for permanents also generalizes. If A is an m × n matrix with m ≤ n, let...

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...

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

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

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...

decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers...

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

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

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

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...

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

matrices are subjected to random permutations many times, with the correlation being recalculated after each permutation. The significance of the observed...

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...

a zero matrix, and k is a scalar. Non-commutative: In general, A ⊗ B and B ⊗ A are different matrices. However, A ⊗ B and B ⊗ A are permutation equivalent...

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...