Title
A Note On The Matrix Arithmetic-Geometric Mean Inequality
Keywords
Matrix inequalities; Positive definite matrices
Abstract
This note proves the following inequality: If n = 3k for some positive integer k, then for any n positive definite matrices A1, A2,…, An, the following inequality holds: (Formula Presented) where ‖ · ‖ represents the operator norm. This inequality is a special case of a recent conjecture proposed by Recht and Ré (2012).
Publication Date
1-1-2018
Publication Title
Electronic Journal of Linear Algebra
Volume
34
Number of Pages
283-287
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.13001/1081-3810.3555
Copyright Status
Unknown
Socpus ID
85055745045 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/85055745045
STARS Citation
Zhang, Teng, "A Note On The Matrix Arithmetic-Geometric Mean Inequality" (2018). Scopus Export 2015-2019. 9301.
https://stars.library.ucf.edu/scopus2015/9301