Fallat, S;
Johnson, CR;
Sokal, AD;
(2017)
Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples.
Linear Algebra and Its Applications
, 520
pp. 242-259.
10.1016/j.laa.2017.01.013.
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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.
| Type: | Article |
|---|---|
| Title: | Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.laa.2017.01.013 |
| Publisher version: | http://dx.doi.org/10.1016/j.laa.2017.01.013 |
| Language: | English |
| Additional information: | © 2017 Elsevier Inc. All rights reserved. This manuscript version is made available under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International license (CC BY-NC-ND 4.0). This license allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licenses are available at https://creativecommons.org/licenses/. Access may be initially restricted by the publisher. |
| Keywords: | Totally positive matrix; Totally nonnegative matrix; Hankel matrix; Stieltjes moment problem; Hadamard product; Hadamard power; Hadamard critical exponent |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1532231 |
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