Nonnegative matrices having nonnegative Drazin pseudoinverses

Abstract

Necessary and sufficient conditions for nonnegative matrices having nonnegative Drazin pseudoinverses are obtained. A decomposition theorem which characterizes the class of all nonnegative matrices with nonnegative Drazin pseudoinverses is proved, thus answering a question raised by several people. It is also shown that if a row (or column) stochastic matrix has a nonnegative Drazin pseudoinverse A(d), then A(d) is some power of A. These results extend known results for nonnegative group-monotone matrices. © 1980.