Total-positivity preservers
arXiv:1711.10468
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.
This paper is being completely rewritten, with the focus now on kernels on arbitrary domains, and the ensuing analysis. This includes Polya frequency functions/sequences, Hankel and other Toeplitz kernels, and the study of their preservers
References in corpus (6)
- Total positivity, Grassmannians, and networks
- Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples
- Preserving positivity for rank-constrained matrices
- On the sign patterns of entrywise positivity preservers in fixed dimension
- Critical exponents of graphs
- Moment-sequence transforms