ELA, Volume 16, pp. 380-388, December 2007, abstract.

Products of M-matrices and Nested Sequences of Principal Minors

D.A. Grundy, C.R. Johnson, D.D. Olesky, and P. van den Driessche

The question of whether or not the product of two n-by-n nonsingular 
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.