How to create covariance matrix when correlation matrix and stddevs are is given

Question

I have the correlation matrix and standard deviations are given and I want to create the covariance matrix.

I can do it programmatically but I want a linear algebraic way...

Thanks in advance

Answer 1

If the elementwise or Hadamard product, which I'll write as $\circ$, is a linear algebraic operation for you, then $C=(\sigma \sigma^T) \circ \Sigma$ where $C$ is the covariance matrix, $\sigma$ is the column vector of standard deviations, and $\Sigma$ is the correlation matrix.

In Matlab syntax:

C=(sigma*sigma').*Sigma