Decomposing a square matrix into two non-square matrices I have a matrix $A$ with dimensions $(m \times m)$ and it is positive definite. I want to find the matrix $B$ with dimensions $(n \times m), (n \ll m)$, which follows the following expression: $$A = B'B$$ Here $B'$ is the transpose of $B$. 
I was also thinking of SVD to re-write $A$ as: $$A = QDQ'$$ but I am not sure how to proceed from there on wards.
Any help to find the matrix $B$ is highly appreciated. 

If the matrix $A$ is real and positive defined, use the Cholesky decomposition.
$$A=B \cdot B'$$
$$B_{j,j}=\sqrt{A_{j,j}-\sum_{k=1}^{j-1} B_{j,k}^2}$$
$$B_{i,j}=\frac{1}{B_{j,j}} \left (A_{i,j}-\sum_{k=1}^{j-1} B_{i,k}B_{j,k} \right)$$
