# nondegeneracy of quadratic space

For a nondegenerate quadratic space $(V,B)$ and $W \subset V$.Prove the followings are equal

(i) $W\bigcap W^\perp =0$.

(ii) $W$ is nondegenerate.

(iii)$W^\perp$ is nondegenerate.

I tried but i couldnt prove it.Could you please help me ?

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I am not sure of the precise terminology here, but on page 14 of J. W. S. Cassels' book "Binary Quadratic Forms", he has what appears to be an identical Lemma, but with "nondegenerate" replaced by "regular". Could that be the same result in different terminology? – Old John Jan 4 '13 at 21:20
Well I dont know but I will check it now :) – Turku Kirli Jan 4 '13 at 21:25
I couldnt find the book :/ Do you have on your PC ? – Turku Kirli Jan 4 '13 at 21:30
I only have a print copy here - but if you want to contact me by email (from my profile) I will see if I can help. – Old John Jan 4 '13 at 21:35
I have sent you a mail.I hope you got it. – Turku Kirli Jan 4 '13 at 21:52