Structure of a nonnegative regular matrix and its generalized inverses

Bapat, R. B. (1998) Structure of a nonnegative regular matrix and its generalized inverses Linear Algebra and its Applications, 268 . pp. 31-39. ISSN 0024-3795

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00243...

Related URL: http://dx.doi.org/10.1016/S0024-3795(97)00062-1

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 AT, the transpose of A. We also obtain the structure of nonnegative matrices which admit nonnegative least-squares and minimum-norm generalized inverses.

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