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

Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...

On the distance from a weakly normal 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...

On condition numbers of polynomial eigenvalue problems with nonsingular leading coefficients

In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition numbers of eigenvalues and the pseudospectral growth rate. We obtain that if a simple eigenvalue of a matrix polynomial is ill-conditioned in some respects, th...

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