Is Every Complex Matrix Similar to Its Transpose?

[arthurhenry]

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

 

[Fredrik]

Did you try to prove it the way micromass suggested the last time you asked? Link.

 

[arthurhenry]

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