Combined matrices of sign regular matrices

The combined matrix of a nonsingular matrix A is the Hadamard (entry wise) product C(A) = A ◦ (A−1)T . Since each row and column sum of C(A) is equal to one, the combined matrix is doubly stochastic when it is nonnegative. In this work, we study the nonnegativity of the combined matrix of sign regular matrices, based upon their signature. In particular, a few coordinates of the signature ε of A play a crucial role in determining whether or not C(A) is nonnegative. © 2014 Elsevier Inc. All rights reserved.

This is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, VOL 498, (2016). DOI 10.1016/j.laa.2014.12.010.