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Matrix similar to its transpose

  1. Aug 12, 2011 #1
    Why is every matrix (complex) similar to its transpose?

    I am looking at a typical jordan block and I see that the transpose of the nilpotent part is again nilpotent and actually similar to the nilpotent part. I can see that the scalar part of the jordan block does not change under transposing, but I still cannot show the result.

    Thank you
  2. jcsd
  3. Aug 12, 2011 #2


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    Did you try to prove it the way micromass suggested the last time you asked? Link.
  4. Aug 12, 2011 #3
    Yes, I did try, and at the time I though I solved it. My problem has been after "reducing the problem to a Jordan block"...

    Thank you
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