New concavity and convexity results for symmetric polynomials and their ratios
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We prove ‘power’ generalizations of Marcus–Lopes style (including McLeod and Bullen) concavity inequalities for elementary symmetric polynomials, and similar generalizations to convexity inequalities of McLeod and Baston for...
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| Format: | Article |
| Language: | English |
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Informa UK Limited
2021
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| Online Access: | https://hdl.handle.net/1721.1/136374.2 |
| _version_ | 1811076784825827328 |
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| author | Sra, Suvrit |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Sra, Suvrit |
| author_sort | Sra, Suvrit |
| collection | MIT |
| description | © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We prove ‘power’ generalizations of Marcus–Lopes style (including McLeod and Bullen) concavity inequalities for elementary symmetric polynomials, and similar generalizations to convexity inequalities of McLeod and Baston for complete homogeneous symmetric polynomials. We also present additional concavity results for elementary symmetric polynomials, of which the main result is a concavity theorem that yields a well-known log-convexity 1972 result of Muir for positive definite matrices as a corollary. |
| first_indexed | 2024-09-23T10:27:32Z |
| format | Article |
| id | mit-1721.1/136374.2 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:27:32Z |
| publishDate | 2021 |
| publisher | Informa UK Limited |
| record_format | dspace |
| spelling | mit-1721.1/136374.22021-11-24T17:30:00Z New concavity and convexity results for symmetric polynomials and their ratios Sra, Suvrit Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We prove ‘power’ generalizations of Marcus–Lopes style (including McLeod and Bullen) concavity inequalities for elementary symmetric polynomials, and similar generalizations to convexity inequalities of McLeod and Baston for complete homogeneous symmetric polynomials. We also present additional concavity results for elementary symmetric polynomials, of which the main result is a concavity theorem that yields a well-known log-convexity 1972 result of Muir for positive definite matrices as a corollary. 2021-11-24T17:29:59Z 2021-10-27T20:35:05Z 2021-11-24T17:29:59Z 2020 2021-04-14T14:41:55Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136374.2 en 10.1080/03081087.2018.1527891 Linear and Multilinear Algebra Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/octet-stream Informa UK Limited arXiv |
| spellingShingle | Sra, Suvrit New concavity and convexity results for symmetric polynomials and their ratios |
| title | New concavity and convexity results for symmetric polynomials and their ratios |
| title_full | New concavity and convexity results for symmetric polynomials and their ratios |
| title_fullStr | New concavity and convexity results for symmetric polynomials and their ratios |
| title_full_unstemmed | New concavity and convexity results for symmetric polynomials and their ratios |
| title_short | New concavity and convexity results for symmetric polynomials and their ratios |
| title_sort | new concavity and convexity results for symmetric polynomials and their ratios |
| url | https://hdl.handle.net/1721.1/136374.2 |
| work_keys_str_mv | AT srasuvrit newconcavityandconvexityresultsforsymmetricpolynomialsandtheirratios |