題組內容
3. Define $e^A = \sum_{k=0}^{\infty} \frac{A^k}{k!}$.
(a) (5 pts) Let \( P^{-1}AP = D \) be a diagonal matrix. Prove that \( e^A = Pe^D P^{-1} \).
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3. Define $e^A = \sum_{k=0}^{\infty} \frac{A^k}{k!}$.
(a) (5 pts) Let \( P^{-1}AP = D \) be a diagonal matrix. Prove that \( e^A = Pe^D P^{-1} \).