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 TaylorsFormulaForMatrixFunctions 2013-03-22 13:39:25 2013-03-22 13:39:25 bwebste (988) bwebste (988) 7 bwebste (988) Theorem msc 47A56