Some interlacing results for indefinite Hermitian matrices
type: Item
instance of: scholarly article
title: Some interlacing results for indefinite Hermitian matrices
zbMATH Open document ID: 0577.15006
DOI: 10.1016/0024-3795(85)90072-2
author: B. Najman
author: Heinz Langer
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: A classical theorem states that the eigenvalues of a principal submatrix of deficiency one of a Hermitian matrix interlace the eigenvalues of the full matrix. The authors consider the similar situation when the underlying inner product is no longer definite. Interlacing no longer holds, eigenvalues may be complex, and the structure of Jordan chains must be considered. In spite of this intricacy there are nontrivial facts concerning the location of the spectrum of the submatrix relative to that of the full matrix. These are too intricate to reproduce here. \{The reviewer's paper, ibid. 14, 135--177 (1976; Zbl 0386.15011) uses a simultaneous reduction for two Hermitian matrices to study similar questions and should be added to the references.\}
reviewed by: Robert C. Thompson
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 3922871
zbMATH Keywords: indefinite inner product
zbMATH Keywords: interlacing inequalities
zbMATH Keywords: principal submatrix
zbMATH Keywords: Hermitian matrix
zbMATH Keywords: Jordan chains
zbMATH Keywords: location of the spectrum
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90072-2
OpenAlex ID: W1966855976
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description: scientific article; zbMATH DE number 3922871