A sin2Θ theorem for graded indefinite Hermitian matrices

This paper gives 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→H=D*(A+ΔA)D. These theorems extend recent results on a definite Hermitian matrix in the graded form (Linear Algebra Appl. 311...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 359; no. 1-3; pp. 263 - 276
Main Authors Truhar, Ninoslav, Li, Ren-Cang
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2003
Subjects
Invariant subspaces
Relative perturbation bounds
Invariant subspaces
Relative perturbation bounds
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ISSN0024-3795
1873-1856
DOI10.1016/S0024-3795(02)00424-X

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Summary:This paper gives 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→H=D*(A+ΔA)D. These theorems extend recent results on a definite Hermitian matrix in the graded form (Linear Algebra Appl. 311 (2000) 45) but the bounds here are more complicated in that they depend on not only relative gaps and norms of ΔA as in the definite case but also norms of some J-unitary matrices, where J is diagonal with ±1 on its diagonal. For two special but interesting cases, bounds on these J-unitary matrices are obtained to show that their norms are of moderate magnitude.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(02)00424-X