Quick question:
I was asked if there exists an invertible matrix $P$ over the complex numbers such that for any matrix $A$:
$PAP^{-1} = A^{T}$
I don't know how to prove it, but I don't think this is true. I know every matrix is similair to its transpose, but it can't be the same matrix $P$ for all matrices...So my gut feeling tells me no, but how do I show it?