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A matrix with 0 determinant whose determinant becomes nonzero when any element on or below the diagonal is changed from 0 to 1. An example is M=[1 -1 0 0; 0 0 -1 0; 1 1 1 -1; ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...

A monotonic matrix of order n is an n×n matrix in which every element is either 0 or contains a number from the set {1,...,n} subject to the conditions 1. The filled-in ...

A strictly upper triangular matrix is an upper triangular matrix having 0s along the diagonal as well as the lower portion, i.e., a matrix A=[a_(ij)] such that a_(ij)=0 for ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

Householder (1953) first considered the matrix that now bears his name in the first couple of pages of his book. A Householder matrix for a real vector v can be implemented ...

An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

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 matrix used in the Jacobi transformation method of diagonalizing matrices. The Jacobi rotation matrix P_(pq) contains 1s along the diagonal, except for the two elements ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...