RELAXING THE NONSINGULARITY ASSUMPTION FOR INTERVALS OF TOTALLY NONNEGATIVE MATRICES

Abstract

Totally nonnegative matrices, i.e., matrices having all their minors nonnegative, and 6 matrix intervals with respect to the checkerboard partial order are considered. It is proven that if the 7 two bound matrices of such a matrix interval are totally nonnegative and satisfy certain conditions, 8 then all matrices from this interval are totally nonnegative and satisfy these conditions, too, hereby 9 relaxing the nonsingularity condition in a former paper [M. Adm, J. Garloff, Intervals of totally 10 nonnegative matrices, Linear Algebra Appl. 439 (2013), pp.3796-3806].