## Implication about positive semidefinite quadratic form [closed]

Let $x^TAx\leq 1$ and $y^TAy\leq 1$; $x,y\in R^{n\times 1}$. $A$ is a positive semidefinite matrix. Does it imply $x^TAy\leq1$?

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 This is a case of Cauchy-Schwarz: $(x^TAy)^2\le(x^TAx)(y^TAy)$. Not appropriate on MO. – Denis Serre Dec 14 at 21:18