# On Symmetric Norm Inequalities And Hermitian Block-Matrices

Abstract : The main purpose of this paper is to englobe some new and known types of Hermitian block-matrices $M=\begin{pmatrix} A & X\\ {X^*} & B\end{pmatrix}$ satisfying or not the inequality $\|M\|\le \|A+B\|$ for all symmetric norms. For positive definite block-matrices another inequality is established and it is shown that it can be sharper (for some symmetric norms) than the following holding inequality $\|M\|\le \|A\|+\|B\|$.
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https://hal.inria.fr/hal-01231860
Contributor : Antoine Mhanna <>
Submitted on : Saturday, May 27, 2017 - 9:50:03 PM
Last modification on : Wednesday, November 13, 2019 - 11:50:04 AM
Document(s) archivé(s) le : Monday, August 28, 2017 - 5:38:53 PM

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### Identifiers

• HAL Id : hal-01231860, version 3
• ARXIV : 1512.03702

### Citation

Antoine Mhanna. On Symmetric Norm Inequalities And Hermitian Block-Matrices. 2016. ⟨hal-01231860v3⟩

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