Let $A \in M_p(\mathbb{K})$ be a diagonalizable matrix. Let $x \in \mathbb{C}$. Show that $E\left(xI_p + A\right)$ exists and that $$E\left(xI_p + A\right) = e^x E(A)$$
Let $A \in M_p(\mathbb{K})$ be a diagonalizable matrix. Let $x \in \mathbb{C}$.
Show that $E\left(xI_p + A\right)$ exists and that
$$E\left(xI_p + A\right) = e^x E(A)$$