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arXiv · 1104.3841

A characterization of Hermitian matrices with variable diagonal and smallest operator norm

Esteban Andruchow·Gabriel Larotonda·Lázaro Recht·Alejandro Varela
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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.

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Esteban Andruchow, Gabriel Larotonda, Lázaro Recht, Alejandro Varela. 2011-04-19. A characterization of Hermitian matrices with variable diagonal and smallest operator norm. https://arxiv.org/abs/1104.3841

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