ADMISSABLE SETS FOR MATRIX EIGENPAIRS

G ALEFELD

goetz.alefeld@mathematik.uni-karlsruhe.de

Institut für Angewandte Mathematik
Universität Karlsruhe
Engkerstaße 2
D-76128 Karlsruhe, Germany

G MAYER

guenter.mayer@mathematik.uni-rostock.de

Fachbereich Mathematik
Universität Rostock
Universitdtsplatz 1
D-18051 Rostock, Germany

Let there be given a real $(n,n)$ matrix $A$ which is the center of an interval matrix $[A- \bigtriangleup A, A+ \bigtriangleup A]= \ :[A].$ We consider the eigenpair sets

$$E=\{(x, \lambda )\in\mathbb{R}^ {n+1} \ \vert \ Ax=\lambda x, A\in[A]\}\\$$

and

       $E_{\cal P}=\{(x, \lambda )\in\mathbb{R}^{n+1}\ \vert \ Ax=\lambda x, A\in[A], A$ has some property $\cal P \}$,

respectively. We discuss several equivalent conditions for a pair $(x, \lambda )$ to belong to $E$ or to $E_{\cal P}$, respectively.