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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 ...

The square root method is an algorithm which solves the matrix equation Au=g (1) for u, with A a p×p symmetric matrix and g a given vector. Convert A to a triangular matrix ...

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 ...

Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

In this work, the name Pythagoras's constant will be given to the square root of 2, sqrt(2)=1.4142135623... (1) (OEIS A002193), which the Pythagoreans proved to be ...

Gaussian elimination is a method for solving matrix equations of the form Ax=b. (1) To perform Gaussian elimination starting with the system of equations [a_(11) a_(12) ... ...