is_positive_semidefinite_matrix

forest.benchmarking.operator_tools.validate_operator.is_positive_semidefinite_matrix(matrix: numpy.ndarray, rtol: float = 1e-05, atol: float = 1e-08) → bool

Checks if a square Hermitian matrix A is positive semi-definite \(eig(A) \geq 0\).

In this numerical implementation we check if each eigenvalue obeys \(eig(A) \geq -|atol|\).

Parameters:

• matrix – a M by M Hermitian matrix.
• rtol – The relative tolerance parameter in np.allclose
• atol – The absolute tolerance parameter in np.allclose

Returns:

True if the matrix is normal; False otherwise.