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Diagonalizability of a matrix A s.t. A^3 = A

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Well, I am constructing a proof for a statement, which builds upon the assumption that a matrix A satisfying A^3 = A is diagonalizable. According to http://crazyproject.wordpress.com/2011/12/08/any-matrix-a-such-that-a³-a-can-be-diagonalized/ this is true, however a reference is made to this "corollary 25 in D&F" (I assume it means Dummit's book in abstract algebra). Unfortunately I don't have access to this book, which makes it more difficult. Is it possible to find that theorem elsewhere, or will I have to work out the Jordan form for A (as can be done when A^2 = A)?

    2. Relevant equations

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    3. The attempt at a solution

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  2. jcsd
  3. Mar 28, 2012 #2

    morphism

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    Hint: A matrix is diagonalizable iff its min poly splits into distinct linear factors.
     
  4. Mar 29, 2012 #3
    Thank you, that would certainly prove the statement.
     
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