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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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Covariance of a vectorized random matrix
In my case, the row covariance matrix is $\mathbf{I}_{n\times n}$ due to the row independence, however, the column covariance instead of being a $n\times n$ matrix is an $n^2\times n^2$ block diagonal. … My question is what is the variance-covariance matrix of the random matrix $\mathbf{A}$ if the covariance of $vec(\mathbf{A}^\intercal)$ is $\boldsymbol{\Sigma}=\text{bdiag}(\boldsymbol{\Sigma}^1,\dots …