STRUCTURE OF A NONNEGATIVE REGULAR MATRIX AND ITS GENERALIZED INVERSES

A nonnegative matrix is called regular if it admits a nonnegative gene ralized inverse. The structure of such matrices has been studied by se veral 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 nonnegati ve generalized inverse of A is dominated by that of A(T), the transpos e of A. We also obtain the structure of nonnegative matrices which adm it nonnegative least-squares and minimum-norm generalized inverses. (C ) 1998 Elsevier Science Inc.