How to find $C$ such that $CC^T =  AA^T + BB^T$, $A$ and $B$ are known.$A = \left(\begin{matrix}X\\Y\end{matrix}\right)$, $B = \left(\begin{matrix}0\\cY\end{matrix}\right)$, $c$ is a constant.To clarify. Cholesky decomposition can give the solution. I was wondering is there any closed form solution?
How to find closed form $C$ such that $CC^T = AA^T + BB^T$
matrix