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The distance from a matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue

✍ Scribed by Nikolaos Papathanasiou; Panayiotis Psarrakos

Book ID: 104037453
Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 803 KB
Volume: 429
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.04.005

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✦ Synopsis

For a matrix polynomial P (λ) and a given complex number μ, we introduce a (spectral norm) distance from P (λ) to the matrix polynomials that have μ as an eigenvalue of geometric multiplicity at least κ, and a distance from P (λ) to the matrix polynomials that have μ as a multiple eigenvalue. Then we compute the first distance and obtain bounds for the second one, constructing associated perturbations of P (λ).

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