Functions and Analysis

   

Function of a Matrix

Authors: Pierre-Yves Gaillard

Let a be a square matrix with complex entries and f a function holomorphic on an open subset U of the complex plane. It is well known that f can be evaluated on a if the spectrum of a is contained in U. We show that, for a fixed f, the resulting matrix depends holomorphically on a.

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[v1] 2012-07-12 01:17:41
[v2] 2013-04-08 09:05:21

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