For any matrix A, does there exist a matrix decomposition such that:
$$ A = Z^T Z $$
A is not necessarily positive definite, so the Cholesky decomposition does not apply.
My motivation for asking this question is because I believe it will allow me to solve the system below for both A and b: $$ A^TA = X^TX+Y^TY\\ A^Tb = X^TP+Y^TQ\\ $$
where all symbols are matrices, except b is a vector.