So I have a vector of asset allocation weights given by $x \in R^4$ and a covariance matrix of the asset returns $\Sigma \in R^{4,4}$. I know by the spectral theorem, $\Sigma = V DV^{-1}$ and the standard deviation of the returns is $\sqrt{x^T \Sigma x}$. Is there any way to use this info and simplify the expression for the standard deviation and remove the square root?
2026-03-31 22:23:38.1774995818
Any way to simplify this expression?
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