Functions and Analysis

1207 Submissions

[2] viXra:1207.0066 [pdf] submitted on 2012-07-18 02:17:26

Matrix Exponential

Authors: Pierre-Yves Gaillard
Comments: 1 Page.

Let a be an element of a finite dimensional C-algebra with 1. Then there is a unique polynomial f_a such that f_a(a) = exp(a) and deg f_a < dim C[a]. We give an explicit formula for f_a.
Category: Functions and Analysis

[1] viXra:1207.0046 [pdf] replaced on 2013-04-08 09:05:21

Function of a Matrix

Authors: Pierre-Yves Gaillard
Comments: 1 Page.

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.
Category: Functions and Analysis