Is the following problem known? Suppose one is given some of the entries of an $n \times n$ matrix $A$ over $\mathbb{R}$, so that the given entries are symmetric. Can one assign values to the remaining entries so that the resulting matrix is positive definite?


Has this problem been studied from a theoretical or algorithmic point of view?



Completing partial matrix to a positive definite matrix
There is an extensive literature. Here are some entry points:


* [Positive definite completions of partial Hermitian matrices](https://www.sciencedirect.com/science/article/pii/0024379584902076)
* [The positive definite completion problem revisited](https://doi.org/10.1016/j.laa.2008.04.020)
* [Matrix Completion Problems](https://www.uibk.ac.at/mathematik/algebra/media/teaching/matrix-completion-problems_entner.pdf)


