Two characterizations of inverse-positive matrices: the Hawkins-Simon condition and the Le Chatelier-Braun principle

Abstract

It is shown that (a weak version of) the Hawkins-Simon condition is satisfied by any real square matrix which is inverse-positive after a suitable permutation of columns or rows. One more characterization of inverse-positive matrices is given converning the Le Chatelier-Braun principle. The proofs are all simple and elementary.