According to duality principle, a bilinear function [itex]\theta:V\times V \rightarrow R[/itex] is equivalent to a linear mapping from V to its dual space V*, which can in turn be represented as a matrix T such that [itex]T(i,j)=\theta(\alpha_i,\alpha_j)[/itex]. And this matrix T is diagonalizable, i.e., [itex]\theta(\alpha_i,\alpha_i)=0,1,-1[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

I don't understand how come [itex]\theta(\alpha_i,\alpha_i)=-1[/itex]

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# Diagonalization of symmetric bilinear function

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