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Covariance is a quantity used to measure the strength and direction of the linear relationship between two variables. The covariance is unscaled, & thus often difficult to interpret; when scaled by the variables' SDs, it becomes Pearson's correlation coefficient.
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Random vector times random matrix
$$ Y_i = \sum_j B_{ij} X_j$$
$$ covar(X_i, X_j) = V_X = \delta_{ij} var(X_i)^2 $$
$$ covar(B_{ij},B_{kl}) \neq 0 $$
$$ V_Y = ? $$
I know, that if $B$ was fixed, it is straight forward, but I would …