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Symmetric Norm Inequalities And Positive Semi-Definite Block-Matrices

Antoine Mhanna 1, *
* Corresponding author
Abstract : For positive semi-definite block-matrix $M,$ we say that $M$ is P.S.D. and we write $M=\begin{pmatrix} A & X\\ {X^*} & B\end{pmatrix} \in {\mathbb{M}}_{n+m}^+$, with $A\in {\mathbb{M}}_n^+$, $B \in {\mathbb{M}}_m^+.$ The focus is on studying the consequences of a decomposition lemma due to C.~Bourrin and the main result is extending the class of P.S.D. matrices $M$ written by blocks of same size that satisfies the inequality: $\|M\|\le \|A+B\|$ for all symmetric norms.
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https://hal.inria.fr/hal-01182244
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Submitted on : Monday, September 14, 2015 - 6:04:31 AM
Last modification on : Tuesday, October 19, 2021 - 11:00:16 AM
Long-term archiving on: : Tuesday, December 29, 2015 - 1:21:15 AM

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  • HAL Id : hal-01182244, version 5
  • ARXIV : 1508.03754

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Antoine Mhanna. Symmetric Norm Inequalities And Positive Semi-Definite Block-Matrices. 2015. ⟨hal-01182244v5⟩

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