1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook