$(x^*Ay)^2 \leq (x^*Ax)(y^*Ay)$
Does this inequality hold for positive semi-definite matrix A? I wonder if this is equivalent to Cauchy-Schwarz Inequality. I tried to diagonalize A but it still half-way towards Cauchy-Schwarz Inequality.
Any thoughts on this inequality? Am I going on the right direction?
Thanks a lot!