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ELA

NORMAL MATRIX POLYNOMIALS WITH NONSINGULAR

LEADING COEFFICIENTS

∗

NIKOLAOS PAPATHANASIOU† AND PANAYIOTIS PSARRAKOS†

Abstract. In this paper, the notions of weakly normal and normal matrixpolynomials with nonsingular leading coefficients are introduced. These matrixpolynomials are characterized using orthonormal systems of eigenvectors and normal eigenvalues. The conditioning of the eigenvalue problem of a normal matrixpolynomial is also studied, thereby constructing an appropriate Jordan canonical form.

Key words. Matrixpolynomial, Normal eigenvalue, Weighted perturbation, Condition number.

AMS subject classifications.15A18, 15A22, 65F15, 65F35.

∗Received by the editors June 25, 2008. Accepted for publication September 11, 2008. Handling

Editor: Michael J. Tsatsomeros.

†Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780

Athens, Greece ([email protected], [email protected]). Electronic Journal of Linear Algebra ISSN 1081-3810

A publication of the International Linear Algebra Society Volume 17, pp. 458-472, September 2008

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