LINEAR TRANSFORMATIONS WHICH MAP THE CLASS OF INVERSE M-MATRICES ONTO ITSELF
Bit-Shun Tam, PO-HONG LIOU · Tamkang Journal of Mathematics · 1990
The purpose of this paper is to characterize those linear transformations on the space of $n \times n$ real matrices which map the class of $n \times n$ inverse $M$- matrices (or, the closure of this class) onto itself. As a by-product of our approach, we also obtain a sufficient condition for an inverse $M$-matrix (resp. $M$-matrix) to have all positive powers being inverse $M$-matrices (resp. $M$-matrices).