"Distance from a weakly normal matrix polynomial to a prescribed multiple eigenvalue" by E. Kokabifar, G.B. Loghmani et al.

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Article Title

On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue

Authors

E. Kokabifar, Yazd UniversityFollow
G.B. Loghmani, Yazd UniversityFollow
Panayiotis Psarrakos, National Technical University of AthensFollow

Keywords

Matrix polynomial, Eigenvalue, Normality, Perturbation, Singular value

Abstract

Consider an$n\times n matrix polynomial P(\lambda). An upper bound for a spectral norm distance from P(\lambda) to the set of n \times n matrix polynomials that have a given scalar μ in C as a multiple eigenvalue was obtained by Papathanasiou and Psarrakos (2008). This paper concerns a refinement of this result for the case of weakly normal matrix polynomials. A modified method is developed and its efficiency is verified by two illustrative examples. The proposed methodology can also be applied to general matrix polynomials.

Recommended Citation

Kokabifar, E.; Loghmani, G.B.; and Psarrakos, Panayiotis. (2016), "On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue", Electronic Journal of Linear Algebra, Volume 31, pp. 71-86.
DOI: https://doi.org/10.13001/1081-3810.2921

abs_vol31_pp71-86.pdf (34 kB)
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Electronic Journal of Linear Algebra