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...

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...

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...

^{-1}\right)=+1.} The sign of a permutation is equal to the determinant of its permutation matrix (below). A permutation matrix is an n × n matrix that has exactly one...

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

example lets us create six permutation matrices (all elements 1 or 0, exactly one 1 in each row and column). The 6x6 matrix representing an element will...

multiples of permutation matrices until we arrive at the zero matrix, at which point we will have constructed a convex combination of permutation matrices...

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

transpose. Specifically, the commutation matrix K(m,n) is the nm × mn permutation matrix which, for any m × n matrix A, transforms vec(A) into vec(AT): K(m...

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...

an n × n {\displaystyle n\times n} matrix is an expression involving permutations and their signatures. A permutation of the set { 1 , 2 , … , 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 = [...

x^{n}-1)} . Any circulant is a matrix polynomial (namely, the associated polynomial) in the cyclic permutation matrix P {\displaystyle P} : C = c 0 I...

are given. G1 and G2 are isomorphic if and only if there exists a permutation matrix P such that P A 1 P − 1 = A 2 . {\displaystyle PA_{1}P^{-1}=A_{2}...

of permutation matrices. One first represents G {\displaystyle G} as a permutation group and then maps each permutation to the corresponding matrix. Representing...

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...

bits are replaced by qubits. The truth table and permutation matrix are as follows (the permutation can be written (7,8) in cycle notation): An input-consuming...

^{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...

and, although not always needed, a permutation matrix (P). It was developed by Prescott Durand Crout. The Crout matrix decomposition algorithm differs slightly...

{\displaystyle P} is a permutation matrix (arising from the need to pivot), L {\displaystyle L} a lower unit triangular matrix, and D {\displaystyle D}...

similarity, if the matrix P can be chosen to be a permutation matrix then A and B are permutation-similar; if P can be chosen to be a unitary matrix then A and...

diagonal entries equal to one, an upper triangular matrix U, and a permutation matrix P; this is a matrix formulation of Gaussian elimination. By the fundamental...

separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations may be characterized...

algorithm) is an algorithm for decomposing a bistochastic matrix into a convex combination of permutation matrices. It was published by Garrett Birkhoff in 1946...

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

the cyclic permutation matrix A = [ 0 1 0 0 0 1 1 0 0 ] . {\displaystyle A={\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix}}.} This matrix shifts the...

within combinatorial matrix theory include: (0,1)-matrix, a matrix whose coefficients are all 0 or 1 Permutation matrix, a (0,1)-matrix with exactly one nonzero...

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...

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

symmetric permutation of the arrowhead matrix, P T A P {\displaystyle P^{T}AP} , where P is a permutation matrix, is a (permuted) arrowhead matrix. Real symmetric...