Citation for the result of variance of quadratic form

155 Views Asked by At

I have seen it expressed that for the quadratic form;

$$ ()=^T+^⊤+ $$

for symmetric $A$, and where $x$ follows multivariate normal,

$$ ∼N(,Σ), \quad ^⊤=. $$

then, $$ Var[()]=2Tr(ΣΣ)+4^⊤Σ+4^⊤Σ+^⊤Σ $$

But I'm struggling to find a publication that contains the proof as a citation. Can anyone help?