Find out if matrix is positive definite with numpy

Question

I need to find out if matrix is positive definite. My matrix is numpy matrix. I was expecting to find any related method in numpy library, but no success. I appreciate any

Answer 1

For a real matrix $A$, we have $x^TAx=\frac{1}{2}(x^T(A+A^T)x)$, and $A+A^T$ is symmetric real matrix. So $A$ is positive definite iff $A+A^T$ is positive definite, iff all the eigenvalues of $A+A^T$ are positive.

import numpy as np

def is_pos_def(A):
    M = np.matrix(A)
    return np.all(np.linalg.eigvals(M+M.transpose()) > 0)