# Canonical form of a general Bilinear Form

There is a simple canonical form of a symmetric and antisymmetric bilibear forms. Is there a canonical form for a general bilinear form?

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To improve your question, why not include in it the canonical forms you have in mind for the first sentence. Also, are you restricting the characteristic in any way (e.g., do you allow bilinear forms in characteristic 2)? –  KConrad Dec 27 '12 at 5:40
This question should have a canonical answer in the literature... Hopefully someone knows! –  Mariano Suárez-Alvarez Dec 27 '12 at 5:54
I think this may be interesting for you: mathoverflow.net/questions/105870/… –  Qfwfq Dec 27 '12 at 13:58
More precisely, the solution when the ground field is $\mathbb{C}$ is stated there. –  Robert Bryant Dec 27 '12 at 14:04