Search Results for ""

Any square matrix A can be written as a sum A=A_S+A_A, (1) where A_S=1/2(A+A^(T)) (2) is a symmetric matrix known as the symmetric part of A and A_A=1/2(A-A^(T)) (3) is an ...

A notation for polyhedra which begins by specifying a "seed" polyhedron using a capital letter. The Platonic solids are denoted T (tetrahedron), O (octahedron), C (cube), I ...

A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, "reduced echelon form" or "row-reduced echelon form." Such a matrix has ...

A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix [A I]=[a_(11) ... a_(1n) 1 0 ... 0; a_(21) ... a_(2n) 0 1 ... 0; | ... | | | ... ...

The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

A method of matrix diagonalization using Jacobi rotation matrices P_(pq). It consists of a sequence of orthogonal similarity transformations of the form ...

Given an m×n matrix A and a p×q matrix B, their Kronecker product C=A tensor B, also called their matrix direct product, is an (mp)×(nq) matrix with elements defined by ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

Consider a knot as being formed from two tangles. The following three operations are called mutations. 1. Cut the knot open along four points on each of the four strings ...

The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...