Relaxing the Nonsingularity Assumption for Intervals of Totally Nonnegative Matrices

Abstract

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