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

On the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues

Consider an n × <span style="fon...

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

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 pertur...

on the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues

consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

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

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field