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Given a symmetric positive definite matrix A, the Cholesky decomposition is an upper triangular matrix U with strictly positive diagonal entries such that A=U^(T)U. Cholesky ...

The vector space generated by the columns of a matrix viewed as vectors. The column space of an n×m matrix A with real entries is a subspace generated by m elements of R^n, ...

Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

The ratio C of the largest to smallest singular value in the singular value decomposition of a matrix. The base-b logarithm of C is an estimate of how many base-b digits are ...

A diagonal matrix D=diag(d_1,...,d_n) sometimes also called the valency matrix corresponding to a graph that has the vertex degree of d_i in the ith position (Skiena 1990, p. ...

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. ...

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 ...

Let P be a matrix of eigenvectors of a given square matrix A and D be a diagonal matrix with the corresponding eigenvalues on the diagonal. Then, as long as P is a square ...

The n×n square matrix F_n with entries given by F_(jk)=e^(2piijk/n)=omega^(jk) (1) for j,k=0, 1, 2, ..., n-1, where i is the imaginary number i=sqrt(-1), and normalized by ...

Fredholm's theorem states that, if A is an m×n matrix, then the orthogonal complement of the row space of A is the null space of A, and the orthogonal complement of the ...