The reverse Cauchy-Schwarz inequality

LetĀ  I be a symmetric, hyperbolic bilinear formĀ (that is, of signature +,+,\dots,+,-) over a finite dimensional real vector space (though this may hold in general as well). If x is positive, meaning I(x,x)>0, then for all y we have

I(x,y)^2 \geq I(x,x)I(y,y).

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The reverse Cauchy-Schwarz inequality