Structure of a nonnegative regular matrix and its generalized inverses

Abstract

A nonnegative matrix is called regular if it admits a nonnegative generalized inverse. The structure of such matrices has been studied by several authors. If A is a nonnegative regular matrix, then we obtain a complete description of all nonnegative generalized inverses of A. In particular, it is shown that if A is a nonnegative regular matrix with no zero row or column, then the zero-nonzero pattern of any nonnegative generalized inverse of A is dominated by that of A^T, the transpose of A. We also obtain the structure of nonnegative matrices which admit nonnegative least-squares and minimum-norm generalized inverses.