Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples
arXiv:1612.02210 · doi:10.1016/j.laa.2017.01.013
Abstract
We show that, for Hankel matrices, total nonnegativity (resp. total positivity) of order r is preserved by sum, Hadamard product, and Hadamard power with real exponent t \ge r-2. We give examples to show that our results are sharp relative to matrix size and structure (general, symmetric or Hankel). Some of these examples also resolve the Hadamard critical-exponent problem for totally positive and totally nonnegative matrices.
LaTex2e, 18 pages; Version 2 incorporates Corrigendum giving a corrected proof of Theorem 3.2