given a symmetric matrix $A_{n\times n}$ and integer $m$, is there any matrix $X_{n\times m}$, s.t., $X\times X^{t}=A$?

Question

Recently I've come across the following problem. I would be very pleased if someone helps me how to deal with. given a symmetric matrix $A_{n\times n}$($n$ is fixed) and positive integer $m$, is there any matrix $X_{n\times m}$, s.t., $X\times X^{t}=A$? My further questions are:

1. If the question has an answer, how many would they be?
2. Can I solve it with the aid of powerful software like Matlab or Python?