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

**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*

**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