gftool.matrix.decompose_hamiltonian

gftool.matrix.decompose_hamiltonian(hamilton) → UDecomposition

Decompose the Hamiltonian matrix into eigenvalues and eigenvectors.

Deprecated since version 0.10.0: Use the function decompose_her.

The similarity transformation:

\[H = U h U^†, \quad h = diag(λ_l)\]

Parameters:

hamilton(…, N, N) complex np.ndarray

Hermitian matrix to be decomposed.

Returns:

Decomposition.rv(…, N, N) complex np.ndarray

The right eigenvectors \(U\).

Decomposition.h(…, N) float np.ndarray

The eigenvalues of hamilton.

Decomposition.rv_inv(…, N, N) complex np.ndarray

The inverse of the right eigenvectors \(U^†\). The Hamiltonian is hermitian, thus the decomposition is unitary \(U^† = U ^{-1}\).