$\Lambda = A^T A$ Decomposition of inverse covariance matrix

Question

Let Precision $\Lambda = S^{-1}$ be defined as inverse covariance matrix. I would like to decompose it as $\Lambda = A^TA$, where $A$ is a square matrix. Covariance and Precision are both positive definite, and all above matrices should be real.

1. How to compute $A$? If $A$ is non-unique, you may introduce any additional constraints to make it unique. The aim is simplicity of computation
2. What is the interpretation of $A$?