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arXiv · 1711.10468

Total-positivity preservers

Alexander Belton·Dominique Guillot·Apoorva Khare·Mihai Putinar
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Abstract

We prove that the only entrywise transforms of rectangular matrices which preserve total positivity or total non-negativity are either constant or linear. This follows from an extended classification of preservers of these two properties for matrices of fixed dimension. We also prove that the same assertions hold upon working only with symmetric matrices; for total-positivity preservers our proofs proceed through solving two totally positive completion problems.

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Alexander Belton, Dominique Guillot, Apoorva Khare, Mihai Putinar. 2017-11-28. Total-positivity preservers. https://arxiv.org/abs/1711.10468

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