This is related to the following question I posted earlier Optimize matrix multiplications
If the values in $E$ are the values of some random variable $X$ and $$x= \frac{v_1^T E v_2}{v_1 ^T M v_2},$$ is the expected value $E[X]$ then how do I compute the variance $Var[X]$ in matrix form?
I tried using the same formula for $x$ but using a matrix where the entries are $(E_{ij}-x)^2$ instead of $E$ according to the variance definition $Var[X] = E[(X-\mu)^2]$. However, I get a different result than if I use the equivalent definition of variance $Var[X] = E[X^2]-(E[X])^2$. In this case I square the entries in $E$ and apply the original formula and subtract $x$ squared.
Thanks.
