On functions that preserve M-matrices and inverse M-matrices
Ravindra B. Bapat, Minerva Catral, Michael Neumann · Linear and Multilinear Algebra · 2005
In earlier works, authors such as Varga, Micchelli and Willoughby, Ando, and Fiedler and Schneider have studied and characterized functions which preserve the M-matrices or some subclasses of the M-matrices, such as the Stieltjes matrices. Here we characterize functions which either preserve the inverse M-matrices or map the inverse M-matrices to the M-matrices. In one of our results we employ the theory of Pick functions to show that if A and B are inverse M-matrices such that B −1 ≤ A −1, then (B+tI)−1 ≤ (A+tI)−1, for all t ≥ 0.