A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices
type: Item
instance of: scholarly article
title: A \(\sin 2\varTheta\) theorem for graded indefinite Hermitian matrices
zbMATH Open document ID: 1025.15028
DOI: 10.1016/S0024-3795(02)00424-X
author: Ninoslav Truhar
author: Ren-Cang Li
published in: Linear Algebra and its Applications
publication date: 2003-03-23T00:00:00Z
review text: The study concerns the double angle theorems that bound the change in an invariant subspace of an indefinite Hermitian matrix in the graded form \(H=D^*AD\) subject to a perturbation \(H\to\widetilde H=D^* (A+\Delta A)D\). These theorems extend a \(\sin 2\theta\) theorem for positive definite Hermitian matrices [Linear Algebra Appl. 311, 45-60 (2000; Zbl 0963.15017)] to indefinite graded Hermitian matrices. The bounds here are more complicated since they depend also on norms of some \(J\)-unitary matrices. Bounds on these \(J\)-unitary matrices are computed.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1886841
zbMATH Keywords: relative perturbation bounds
zbMATH Keywords: invariant subspaces
zbMATH Keywords: hyperbolic singular value decomposition
zbMATH Keywords: \(J\)-unitary matrices
zbMATH Keywords: double angle theorems
zbMATH Keywords: indefinite Hermitian matrix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1886841