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Product of Diagonalizable matrices

  1. Nov 18, 2012 #1
    Ignore post, I found a counterexample to (2).

    I'm studying for an upcoming exam, and I'm a bit confused about how to go about proving or disproving the statement (2).

    1.) Products of diagonalizable matrices are never diagonalizable.

    I figured false and my counterexample is really just the square of the identity matrix. Since I is diagonalizable and I^2=I.

    2.) Productions of diagonalizable matrices are always diagonalizable.

    I'm not too sure if it's true to begin with. Trying to construct a counterexample for 2x2 matrices hasn't been successful yet. Any hints much appreciated.
     
    Last edited: Nov 18, 2012
  2. jcsd
  3. Nov 19, 2012 #2

    HallsofIvy

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    A matrix, A, on Rn, is "diagonalizable" if and only if there exist a basis for Rn consisting of eigenvectors of A. Can you use that?
     
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