Perturbation thèorems for the generalized eigenvalue problem
Copyright policy )Perturbation thèorems for the generalized eigenvalue problem
AbstractGiven a matrix pair Z = (A, B), the perturbation of its eigenvalues (α, β) is studied. Considering two pairs Z, W as points of the Grassman manifold Gn, 2n and its eigenvalues as points in G1, 2, the projective complex plane, the distance of the spectra, measured in the chordal metric in G1, 2, is bounded by some distance of the matrix pairs in Gn, 2n. Analogs of the Bauer-Fike theorem, Henrici's theorem, and the Hoffman-Weilandt theorem are obtained, from which the “classical” results can be derived.
- Bielefeld University Germany
- Academia Sinica Taiwan
normal matrix, generalized eigenvalue problem, Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, perturbation of eigenvalues, Inequalities involving eigenvalues and eigenvectors, matrix pair, 510, Discrete Mathematics and Combinatorics, Hermitian, skew-Hermitian, and related matrices, Geometry and Topology, spectral difference, Grassmann manifold
normal matrix, generalized eigenvalue problem, Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, perturbation of eigenvalues, Inequalities involving eigenvalues and eigenvectors, matrix pair, 510, Discrete Mathematics and Combinatorics, Hermitian, skew-Hermitian, and related matrices, Geometry and Topology, spectral difference, Grassmann manifold
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