Products of M-matrices and nested sequences of principal minors

Abstract

The question of whether or not the product of two nonsingular n-by-n M-matrices has
a nested sequence of positive principal minors (abbreviated to a nest) is considered. For n = 2, 3, 4
such a product always has a nest, and this is conjectured for n = 5. For general n, examples of
products of two M-matrices with specified structure are identified as having a leading or trailing
nest. For n = 4, it is shown that the cube of an M-matrix need not have a nest.