Taylor’s formula for matrix functions

Let $p$ be a polynomial and suppose $\mathbf{A}$ and $\mathbf{B}$ commute, i.e. $\mathbf{A}\mathbf{B}=\mathbf{B}\mathbf{A}$ , then

$p(\mathbf{A}+\mathbf{B})=\sum_{k=0}^{n}\frac{1}{k!}p^{(k)}(\mathbf{A})\mathbf{% B}^{k}.$

where $n=\deg(p)$ .

Title	Taylor’s formula for matrix functions
Canonical name	TaylorsFormulaForMatrixFunctions
Date of creation	2013-03-22 13:39:25
Last modified on	2013-03-22 13:39:25
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	7
Author	bwebste (988)
Entry type	Theorem
Classification	msc 47A56