I am trying to find the following matrix, $B$ using the following matrix equation,
\begin{equation} A = B^{T}CB \end{equation}
where we have the matrices A and C. I know that $B^{T}=B$, but trying to use a $2$ x $2$ matrix for each of the matrices, respectively, representing $B$ symbolically only I am left with $2$, $2$ x $2$ matrices on each side of the equality. Is there any literature for a general way for solving this matrix equation? Thank you