Strong majorization for Hermitian matrices
type: Item
instance of: scholarly article
title: Strong majorization for Hermitian matrices
zbMATH Open document ID: 0881.15008
DOI: 10.1016/S0024-3795(96)00029-8
author: Miroslav Fiedler
author: Vlastimil Pták
published in: Linear Algebra and its Applications
publication date: 1998-01-25T00:00:00Z
review text: This paper concerns a partial characterization of \(G<_aF\) \((F\) is the real part of some matrix similar to \(G)\) and \(\widetilde G<_m \widetilde F\) \((\widetilde F\) is the modulus of some matrix similar to \(\widetilde G\); \(\widetilde F\), \(\widetilde G\) positive definite). The latter implies that the spectrum \(\sigma(\widetilde F)\) multiplicatively majorizes \(\sigma (\widetilde G)\). The converse is not true. Let \(G\) be real diagonal with all diagonal entries different, and let \(F\) be arbitrary Hermitian. Then \(\sigma (F)\) majorizes \(\sigma (G)\) if and only if \(G<_a F\). For diagonalizable matrices these conditions are equivalent to known multiplicative and additive spectral majorization conditions.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 999977
zbMATH Keywords: Hermitian matrix
zbMATH Keywords: spectrum
zbMATH Keywords: spectral majorization
reviewed by: Erwin O. Kreyszig
MaRDI profile type: Publication
cites work: Q4169818
cites work: Log majorization and complementary Golden-Thompson type inequalities
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description: scientific article; zbMATH DE number 999977