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

Socpus ID

85055745045 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85055745045

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