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A completely positive matrix is a real n×n square matrix A=(a_(ij)) that can be factorized as A=BB^(T), where B^(T) stands for the transpose of B and B is any (not ...

A copositive matrix is a real n×n square matrix A=(a_(ij)) that makes the corresponding quadratic form f(x)=x^(T)Ax nonnegative for all nonnegative n-vectors x. Copositive ...

A doubly nonnegative matrix is a real positive semidefinite n×n square matrix with nonnegative entries. Any doubly nonnegative matrix A of order n can be expressed as a Gram ...

Relaxation methods are methods of solving partial differential equations that involve splitting the sparse matrix that arises from finite differencing then iterating until a ...

A matrix whose entries are polynomials.

The conjugate gradient method can be applied on the normal equations. The CGNE and CGNR methods are variants of this approach that are the simplest methods for nonsymmetric ...

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.

The matrix operations of 1. Interchanging two rows or columns, 2. Adding a multiple of one row or column to another, 3. Multiplying any row or column by a nonzero element.

The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors.

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...