I would like to check whether a matrix $A$ is positive definite. Previous answers to this question have pointed to the Cholesky decomposition. However, since my framework of choice is Tensorflow, I cannot catch and handle the exception thrown when the decomposition discovers that the matrix is not positive definite, so I need another way.
Another approach I have seen is to compute the eigenvalues, and check whether any of them are negative. This works, but it is slow. I have also heard the suggestion to compute the smallest eigenvalue. This makes sense to me -- if it is negative, we know the matrix is not positive definite -- but I am unsure how to do this efficiently. I would be grateful for some pointers!