gem.utility.utilities.Hermitian_list

gem.utility.utilities.Hermitian_list(N: int, *, dtype=<class 'numpy.complex128'>)

Return an orthonormal (Hilbert–Schmidt) basis of N×N Hermitian matrices.

Basis elements:

• Diagonal: E_ii

• Off-diagonal symmetric: (E_ij + E_ji)/sqrt(2)

• Off-diagonal antisymmetric: i(E_ij - E_ji)/sqrt(2)

Also returns a list of plain transposes (not conjugate transposes), matching the original code’s tH_list behavior.

Parameters:

Nint

Matrix dimension.

dtypenumpy dtype

Output dtype (default complex128).

Returns:

H_listlist[np.ndarray]

Hermitian basis matrices, length N^2.

tH_listlist[np.ndarray]

Plain transpose of each basis matrix, length N^2.