eig

• full name: tenpy.linalg.np_conserved.eig

• parent module: tenpy.linalg.np_conserved

• type: function

tenpy.linalg.np_conserved.eig(a, sort=None)

Calculate eigenvalues and eigenvectors for a non-hermitian matrix.

W, V = eig(a) yields \(a V = V diag(w)\).

Parameters

aArray

The hermitian square matrix to be diagonalized.

sort{‘m>’, ‘m<’, ‘>’, ‘<’, None}

How the eigenvalues should are sorted within each charge block. Defaults to None, which is same as ‘<’. See argsort() for details.

Returns

W1D ndarray

The eigenvalues, sorted within the same charge blocks according to sort.

VArray

Unitary matrix; V[:, i] is normalized eigenvector with eigenvalue W[i]. The first label is inherited from A, the second label is 'eig'.

Notes

Requires the legs to be contractible. If a is not blocked by charge, a blocked copy is made via a permutation P, :math:` a’ = P a P = V’ W’ (V’)^{dagger}`. The eigenvectors V are then obtained by the reverse permutation, \(V = P^{-1} V'\) such that A = V W V^{dagger}.