gftool.matrix.decompose_hamiltonian¶
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gftool.matrix.decompose_hamiltonian(hamilton) → gftool.matrix.UDecomposition[source]¶ 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 \(U^† = U ^{-1}\)