qit.utils.spectral_decomposition

qit.utils.spectral_decomposition(A: array[complex], tol: float = 1e-08) → tuple[array[float], list[array[complex]]]

Spectral decomposition of a Hermitian matrix.

Parameters

• A (array[complex]) – Hermitian matrix to decompose

• tol (float) – numerical tolerance

Returns

unique eigenvalues a and the corresponding projectors P for A, such that \(A = \sum_k a_k P_k\).

Return type

tuple[‘array[float]’, list[‘array[complex]’]]