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Homework Help: Proving diagonalizability with the power series

  1. Feb 27, 2010 #1
    1. The problem statement, all variables and given/known data
    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).

    2. Relevant equations

    3. 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!
  2. jcsd
  3. Feb 27, 2010 #2


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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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