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I am trying to see how to classify all symmetric bilinear forms B on R^3 as a V.Space

over the reals.

My idea is to use the standard basis for R^3 , then use the matrix representation M

=x^T.M.y . Then, since M is, by assumption, symmetric, we can diagonalize M.

So it seems all symmetric bilinear forms are just all diagonal matrices; maybe we

need to factor out those that are equivalent as bilinear forms, i.e., B,B' are equivalent

if there is a linear isomorphism L:R^3-->R^3 with B(v)=B'(L(v)).

Is this right? Is there anything else?

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# Classifying Symmetric Quadratic Forms

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