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Preprints, Working Papers, ... Year : 2015

Symmetric Norm Inequalities And Positive Semi-Definite Block-Matrices

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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Dates and versions

hal-01182244 , version 1 (14-08-2015)
hal-01182244 , version 2 (15-08-2015)
hal-01182244 , version 3 (18-08-2015)
hal-01182244 , version 4 (19-08-2015)
hal-01182244 , version 5 (14-09-2015)

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Cite

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

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