Matrix polynomial, Eigenvalue, Normality, Perturbation, Singular value
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.
Kokabifar, E.; Loghmani, G.B.; and Psarrakos, Panayiotis.
"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.