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The result of a matrix multiplication.

There are two equivalent definitions for a nilpotent matrix. 1. A square matrix whose eigenvalues are all 0. 2. A square matrix A such that A^n is the zero matrix 0 for some ...

A k-matrix is a kind of cube root of the identity matrix (distinct from the identity matrix) which is defined by the complex matrix k=[0 0 -i; i 0 0; 0 1 0]. It satisfies ...

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...

Consider the number of sequences that can be formed from permutations of a set of elements such that each partial sum is nonnegative. The number of sequences with nonnegative ...

A diagonal matrix whose diagonal elements all contain the same scalar lambda. A scalar matrix is therefore equivalent to lambdaI, where I is the identity matrix.

A square matrix which is not reducible is said to be irreducible.

Matrix decomposition refers to the transformation of a given matrix (often assumed to be a square matrix) into a given canonical form.

An n×n matrix A is an elementary matrix if it differs from the n×n identity I_n by a single elementary row or column operation.

A square matrix A is called diagonally dominant if |A_(ii)|>=sum_(j!=i)|A_(ij)| for all i. A is called strictly diagonally dominant if |A_(ii)|>sum_(j!=i)|A_(ij)| for all i. ...