New concavity and convexity results for symmetric polynomials and their ratios
Name
1803.10141.pdf
Description
Submitted version
Size
204.06 KB
Format
Unknown
Checksum (MD5)
7951c5e7cf174486af9270e785ce0cab
Author(s)
Sra, Suvrit
Date Issued
2020
Journal
Linear and Multilinear Algebra
Publisher
Informa UK Limited
Version
Original manuscript
Abstract
© 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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1080/03081087.2018.1527891
