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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 ?

Turku Kirli
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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 04 '13 at 21:20
  • Well I dont know but I will check it now :) – Turku Kirli Jan 04 '13 at 21:25
  • I couldnt find the book :/ Do you have on your PC ? – Turku Kirli Jan 04 '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 04 '13 at 21:35
  • I have sent you a mail.I hope you got it. – Turku Kirli Jan 04 '13 at 21:52
  • Dear Turku, Do you know the definitions of the various concepts? For example, what does it mean for $W$ to be degenerate? Regards, – Matt E Jan 05 '13 at 01:03

1 Answers1

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maybe you can look at here: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$

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Serkan Yaray
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