M math8 Feb 2009 98 0 May 17, 2010 #1 If P is a Hermitian positive definite nxn matrix, is it true that \(\displaystyle (x^{*}Px)^{2} = \left\| x \right\|^{2}_{2} x^{*}P^{2}x\) for all \(\displaystyle x \in C^{n}\) ?

If P is a Hermitian positive definite nxn matrix, is it true that \(\displaystyle (x^{*}Px)^{2} = \left\| x \right\|^{2}_{2} x^{*}P^{2}x\) for all \(\displaystyle x \in C^{n}\) ?