TY - JOUR
T1 - Lipschitz stability of canonical Jordan bases of H-selfadjoint matrices under structure-preserving perturbations
AU - Bella, T.
AU - Olshevsky, V.
AU - Prasad, U.
PY - 2008/4/15
Y1 - 2008/4/15
N2 - In this paper we study Jordan-structure-preserving perturbations of matrices selfadjoint in the indefinite inner product. The main result of the paper is Lipschitz stability of the corresponding affiliation matrices. The result can be reformulated as Lipschitz stability, under small perturbations, of canonical Jordan bases (i.e., eigenvectors and generalized eigenvectors enjoying a certain flipped orthonormality relation) of matrices selfadjoint in the indefinite inner product. The proof relies upon the analysis of small perturbations of invariant subspaces, where the size of a permutation of an invariant subspace is measured using the concepts of a gap and of a semigap.
AB - In this paper we study Jordan-structure-preserving perturbations of matrices selfadjoint in the indefinite inner product. The main result of the paper is Lipschitz stability of the corresponding affiliation matrices. The result can be reformulated as Lipschitz stability, under small perturbations, of canonical Jordan bases (i.e., eigenvectors and generalized eigenvectors enjoying a certain flipped orthonormality relation) of matrices selfadjoint in the indefinite inner product. The proof relies upon the analysis of small perturbations of invariant subspaces, where the size of a permutation of an invariant subspace is measured using the concepts of a gap and of a semigap.
KW - Canonical Jordan bases
KW - Gaps
KW - Indefinite inner product
KW - Invariant subspaces
KW - Perturbations
KW - Structure-preserving perturbations
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U2 - 10.1016/j.laa.2007.11.023
DO - 10.1016/j.laa.2007.11.023
M3 - Article
AN - SCOPUS:39549115886
SN - 0024-3795
VL - 428
SP - 2130
EP - 2176
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 8-9
ER -