The distance from a matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue 1
Νικόλαος Παπαθανασίου, Panayiotis Psarrakos · 2008
For a matrix polynomial P(�) and a given complex number µ, we introduce a (spectral norm) distance from P(�) to the matrix polynomials that have µ as an eigenvalue of geometric multiplicity at least �, and a distance from P(�) 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(�).