Comparision of tensor product and cartesian product

cartesian.py

import itertools

def cartesian_product_vectors(vector1, vector2):
    product = list(itertools.product(vector1, vector2))
    return product

def cartesian_product_scalar(scalar1, scalar2):
    return cartesian_product_vectors([scalar1], [scalar2])

scalar_a = 2
scalar_b = 3
result = cartesian_product_scalar(scalar_a, scalar_b)
print(f"{scalar_a} × {scalar_b} = {result}")

vector_a = [1, 2]
vector_b = [1, 2]
result = cartesian_product_vectors(vector_a, vector_b)
print(f"{vector_a} × {vector_b} = {result}")

comparison.txt

konard@konard-MS-7982:~/Desktop/products$ python3 tensor.py
2 ⊗ 3 = 6
[1 2] ⊗ [1 2] = [[1 2] [2 4]]
konard@konard-MS-7982:~/Desktop/products$ python3 cartesian.py 
2 × 3 = [(2, 3)]
[1, 2] × [1, 2] = [(1, 1), (1, 2), (2, 1), (2, 2)]

tensor.py

import numpy as np

# Scalar tensor product (simply multiplication)
scalar1 = 2
scalar2 = 3
tensor_product_scalars = scalar1 * scalar2
print(f"{scalar1} ⊗ {scalar2} = {tensor_product_scalars}")

# Vector tensor product (outer product)
vector1 = np.array([1, 2])
vector2 = np.array([1, 2])
tensor_product_vectors = np.outer(vector1, vector2)
print(f"{vector1} ⊗ {vector2} = {tensor_product_vectors}")