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...

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

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 = [...

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

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...

}+\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 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...

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

^{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...

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

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

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

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...

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...

multilinear in the rows and columns of the matrix; and the immanant is invariant under simultaneous permutations of the rows or columns by the same element...

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...

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

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

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

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

Friedrich Gauss, have worked on both the eight queens puzzle and its generalized n-queens version. In 1874, S. Günther proposed a method using determinants...

statistics, the class of vector generalized linear models (VGLMs) was proposed to enlarge the scope of models catered for by generalized linear models (GLMs). In...

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...

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...