Bilinear forms

  • #1
I'm trying to study geometric algebra using Artin's book and am having some difficulty with what degenerate symmetric bilinear forms would be like. Does someone know of an example and brief explanation. Also, the opposite being "nondegenerate nonsymmetric bilinear form" would help me out. If I have one explanation, that will probably help me enough though. I apologize, but sometimes I don't get everything in self study. Thanks!
 

Answers and Replies

  • #2
Office_Shredder
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Google is your friend

http://en.wikipedia.org/wiki/Degenerate_form

Popped up as the second or third hit

Similarly for non-symmetric bilinear forms

http://en.wikipedia.org/wiki/Bilinear_form
A bilinear form is symmetric if and only if the maps B1,B2: V -> V* are equal, and skew-symmetric if and only if they are negatives of one another. If char(F) ≠ 2 then one can always decompose a bilinear form into a symmetric and a skew-symmetric part as follows
where you can find the definitions of the Bi earlier in the article
 

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