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For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

The Cayley-Purser algorithm is a public-key cryptography algorithm that relies on the fact that matrix multiplication is not commutative. It was devised by Sarah Flannery ...

Given a matrix A, its QR-decomposition is a matrix decomposition of the form A=QR, where R is an upper triangular matrix and Q is an orthogonal matrix, i.e., one satisfying ...

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

The bandwidth of a matrix M=(m_(ij)) is the maximum value of |i-j| such that m_(ij) is nonzero.

The Drazin inverse is a matrix inverse-like object derived from a given square matrix. In particular, let the index k of a square matrix be defined as the smallest ...

A Hessenberg decomposition is a matrix decomposition of a matrix A into a unitary matrix P and a Hessenberg matrix H such that PHP^(H)=A, where P^(H) denotes the conjugate ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

The Hilbert-Schmidt norm of a matrix A is a matrix norm defined by ||A||_(HS)=sqrt(sum_(i,j)a_(ij)^2).

An n×n array is called a square array. Considered as a matrix, a square array is called a square matrix.