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ELA

PERTURBATIONS OF FUNCTIONS OF

DIAGONALIZABLE MATRICES

∗

MICHAEL I. GIL’†

Abstract. LetAand ˜Aben×ndiagonalizable matrices andf be a function defined on their

spectra. In the present paper, bounds for the norm off(A)−f( ˜A) are established. Applications to

differential equations are also discussed.

Key words. Matrix valued functions, Perturbations, Similarity of matrices, Diagonalizable matrices.

AMS subject classifications.15A54, 15A45, 15A60.

∗Received by the editors December 8, 2009. Accepted for publication April 19, 2010. Handling

Editor: Peter Lancaster.

†Department of Mathematics, Ben Gurion University of the Negev, P.0. Box 653, Beer-Sheva

84105, Israel ([email protected]). Supported by the Kameah fund of the Israel. Electronic Journal of Linear Algebra ISSN 1081-3810

A publication of the International Linear Algebra Society Volume 20, pp. 303-313, May 2010

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