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Given an m×n matrix B, the Moore-Penrose generalized matrix inverse is a unique n×m matrix pseudoinverse B^+. This matrix was independently defined by Moore in 1920 and ...

Three types of n×n matrices can be obtained by writing Pascal's triangle as a lower triangular matrix and truncating appropriately: a symmetric matrix S_n with (S)_(ij)=(i+j; ...

A positive semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonnegative. A matrix m may be tested to determine if it is positive semidefinite in the ...

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 ...

A sparse matrix is a matrix that allows special techniques to take advantage of the large number of "background" (commonly zero) elements. The number of zeros a matrix needs ...

A square matrix A is a special orthogonal matrix if AA^(T)=I, (1) where I is the identity matrix, and the determinant satisfies detA=1. (2) The first condition means that A ...

A square matrix U is a special unitary matrix if UU^*=I, (1) where I is the identity matrix and U^* is the conjugate transpose matrix, and the determinant is detU=1. (2) The ...

A matrix for a round-robin tournament involving n players competing in n(n-1)/2 matches (no ties allowed) having entries a_(ij)={1 if player i defeats player j; -1 if player ...

A zero matrix is an m×n matrix consisting of all 0s (MacDuffee 1943, p. 27), denoted 0. Zero matrices are sometimes also known as null matrices (Akivis and Goldberg 1972, p. ...

The correlation coefficient, sometimes also called the cross-correlation coefficient, Pearson correlation coefficient (PCC), Pearson's r, the Perason product-moment ...