Negativity-preserving transforms of tuples of symmetric matrices

[2310.18041] Negativity-preserving transforms of tuples of symmetric matrices Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Classical Analysis and ODEs arXiv:2310.18041 (math) [Submitted on 27 Oct 2023 ( v1 ), last revised 19 Mar 2026 (this version, v4)] Title: Negativity-preserving transforms of tuples of symmetric matrices Authors: Alexander Belton , Dominique Guillot , Apoorva Khare , Mihai Putinar View a PDF of the paper titled Negativity-preserving transforms of tuples of symmetric matrices, by Alexander Belton and 3 other authors View PDF HTML (experimental) Abstract: 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 relying on well chosen test matrices, Sidon sets from number theory, and analytic properties of absolutely monotone functions. We continue with the analogous classification in the multi-variable setting, revealing for the first time a striking separation of variables, with absolute monotonicity on one side and only homotheties on the other. We conclude with the complex analogue of this result. Comments: Minor revisions. Final version, to appear in Proceedings of the London Mathematical Society Subjects: Classical Analysis and ODEs (math.CA) ; Functional Analysis (math.FA) MSC classes: 15B48 (primary), 15A18, 26A48, 32A05 (secondary) Cite as: arXiv:2310.18041 [math.CA] (or arXiv:2310.18041v4 [math.CA] for this version) https://doi.org/10.48550/arXiv.2310.18041 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Proceedings of the London Mathematical Society 132 (2026), no. 4, art. # e70147, 46 pp Related DOI : https://doi.org/10.1112/plms.70147 Focus to learn more DOI(s) linking to related resources Submission history From: Apoorva Khare [ view email ] [v1] Fri, 27 Oct 2023 10:37:55 UTC (36 KB) [v2] Wed, 22 Nov 2023 18:35:31 UTC (36 KB) [v3] Thu, 27 Jun 2024 03:32:53 UTC (44 KB) [v4] Thu, 19 Mar 2026 11:41:17 UTC (45 KB) Full-text links: Access Paper: View a PDF of the paper titled Negativity-preserving transforms of tuples of symmetric matrices, by Alexander Belton and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.CA < prev | next > new | recent | 2023-10 Change to browse by: math math.FA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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