In the book that I'm reading there is this one theorem which states.
Let V be a finite-dimensional vector space over a field F not of characteristic two. Then every symmetric bilinear form on V is diagonalizable.
I was wondering whether the converse is also true.
Meaning does a bilinear form being diagonalizable imply that the bilinear form was symmetric.
If it doesn't do you mind giving an explicit bilinear form where it doesn't hold true.