A characterization of Hermitian matrices with variable diagonal and smallest operator norm
Operator Algebras
2011-04-20 v1
Abstract
We describe properties of a Hermitian square matrix M in M_n(C) equivalent to that of having minimal quotient norm in the following sense: ||M|| <= ||M+D|| for all real diagonal matrices D in M_n(C) and || || the operator norm. These matrices are related to some particular positive matrices with their range included in the eigenspaces of the eigenvalues +||M|| and -||M|| of M. We show how a constructive method can be used to obtain minimal matrices of any dimension relating this problem with majorization results in R^n.
Keywords
Cite
@article{arxiv.1104.3841,
title = {A characterization of Hermitian matrices with variable diagonal and smallest operator norm},
author = {Esteban Andruchow and Gabriel Larotonda and Lázaro Recht and Alejandro Varela},
journal= {arXiv preprint arXiv:1104.3841},
year = {2011}
}
Comments
9 pages