Given that $\Sigma_{n\times n}$ and $S_{n\times n}$ are symmetric matrices while $B$ is a non-symmetric square matrix, solve for $\Sigma$ in the equation $$B\Sigma+\Sigma B^{T}=-S$$
This looks so simple but I can't seem to figure out how to solve it. I was imagining using the skew matrices property $\Sigma B^{T}=(B\Sigma)^{T}=-B\Sigma$ which seems to make everything trivial. I will appreciate if someone can help me solve the problem or at least provide some hint.