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[Community Question] Linear-algebra: Solving matrix equation C=A*B*Atranspose

One of our user asked:

I am writing a code on Matlab to calculate the matrix $B$, given $C$ and $A$, following the equation

$$C=A B A^\mathrm{T}$$

$A^\mathrm{T}$ is non-invertible, so I can't just multiply $C$ by the inverse of the matrices.

I can't solve this by hand either because $C$ is a 3144x3144 matrix...any help will be greatly appreciated!


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