On the Variation of the Spectra of Matrix Pencils
نویسنده
چکیده
Several “distances” between the spectra of two regular matrix pencils are discussed and compared. The relations obtained enable us to estimate upper bounds on one “distance” via known upper bounds on others. We also give some perturbation bounds and then show how to apply the relations obtained in this note.
منابع مشابه
On perturbations of matrix pencils with real spectra. II
A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A and à be two n×n Hermitian matrices, and let λ1, . . . , λn and λ̃1, . . . , λ̃n be their eigenvalues arranged in ascending order. Then ∣∣∣∣∣∣diag (λ1 − λ̃1, . . . , λn − λ̃n)∣∣∣∣∣∣ ≤ ∣∣∣∣∣∣A− Ã∣∣∣∣∣∣ for any unitarily invariant norm ||| · |||. In this paper, we generalize this to the perturbation ...
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