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Does diagonalizable imply symmetric?

  1. Apr 10, 2012 #1
    In order to prove my PDE system is well-posed, I need to show that if a matrix is diagonalizable and has only real eigenvalues, then it's symmetric.

    2. Relevant equations
    I've found theorems that relate orthogonally diagonalizable and symmetric matrices, but is that sufficient?

    3. The attempt at a solution
    See above.
  2. jcsd
  3. Apr 10, 2012 #2
    It's not true. Consider the matrix

    [tex]\left(\begin{array}{cc} 1 & 2\\ 0 & 3\end{array}\right)[/tex]
  4. Apr 10, 2012 #3
    Darn.. well I guess to find another way to show the PDE is well-posed.
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