Negativity-preserving transforms of tuples of symmetric matrices

Autor:	Belton, Alexander, Guillot, Dominique, Khare, Apoorva, Putinar, Mihai
Rok vydání:	2023
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis 15B48 (primary) 15A18 26A48 32A05 (secondary)
Druh dokumentu:	Working Paper
Popis:	Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining recent advances in matrix analysis with some novel arguments using well chosen test matrices. We continue with the analogous classification in the multi-variable setting, revealing a striking separation of variables, with absolute monotonicity on one side and homotheties on the other. We conclude with the complex analogue of this result. Comment: 42 pages, no figures, LaTeX. (1) Results significantly strengthened, by removing all restrictions on the target negative inertia "l". Significant edits to the exposition (except Section 3 and Appendix A). (2) The previous "Theorems B and C" are merged into a unified Theorem B. (3) A new Theorem C and Section 6 are added, working out the analoguous results for complex Hermitian matrices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.18041 Zobrazit plný text záznamu View this record from Arxiv