inner_product.py

import numpy as np

M = 4
N = 4

GAMMA = np.diag(np.exp(-1j * np.arange(M) * 2 * np.pi / M))
DELTA = np.diag(np.exp(1j * np.arange(N) * 2 * np.pi / N))

def gamma_deriv(GAMMA, n):
    return np.diag((-np.arange(M) * 1j * 2 * np.pi / M))**n @ GAMMA
def delta_deriv(DELTA, n):
    return np.diag((np.arange(N) * 1j * 2 * np.pi / N))**n @ DELTA

def frobenius_inner_product(A, B):
    return np.trace(A.T.conj() @ B)

print(frobenius_inner_product(GAMMA**3, gamma_deriv(GAMMA, 3)))