= Indefinite quadratic form
{title2=$q(u)>0,\quad q(v)<0$}
A real <quadratic form> is indefinite when it takes both positive and negative values. For a real <symmetric matrix> representing it, this means that its <eigenvalues> include both signs. For example, $q(x,y)=x^2-y^2$ has $q(1,0)=1$ and $q(0,1)=-1$; a zero value at the nonzero <vector> $(1,1)$ does not imply <positive semidefiniteness>.<Bilinear Forms by Keith Conrad>[Definition 6.21 and footnote 6, p. 40: definiteness and a nondegenerate indefinite example]{ref}
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