# Rank of a bilinear form

I have to prove that a bilinear form $B$ has full rank, and I would like to know some ideas on how to prove that.

Can anyone give an idea?

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Hint. Show that a bilinear map is non-degenerate if and only if its matrix representation has full rank.

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The problem is that is very hard to find a matrix representation (I am working with a particular bilineal form, but i want some alternative ideas instead of asking for the solution, because i would like to think the problem by my self –  Dimitri Feb 24 '13 at 22:08
@Dimitri Can you prove that it's non-degenerate? (That is $\langle x,y\rangle = 0$ for all $y$ implies that $x=0$.) –  Alexander Gruber Feb 26 '13 at 1:16
Yes, that is what i try to do, with a little help and work i think i almost have it :) –  Dimitri Feb 26 '13 at 1:20