# The reverse Cauchy-Schwarz inequality

Let  $I$ be a symmetric, hyperbolic bilinear form (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

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