Proving diagonalizability with the power series

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rugbygirl2
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Homework Statement


If A is a diagonal matrix with the diagonal entries a1, a2, ..., an, use the power series to prove that exp(At) is a diagonal matrix with the entries exp(a1t), exp(a2t), ..., exp(ant).


Homework Equations





The Attempt at a Solution


I can prove that A is diagonalizable with T-1 AT=D, but I'm not sure how to begin the proof using the power series as a method. My book does not discuss this and any insight would be greatly appreciated, thanks!
 

Answers and Replies

  • #2
Dick
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You don't have to diagonalize A. It's already diagonal. You just have to realize that the power series of A is the same as the power series of the diagonal elements.
 

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