Why are standard matrix multiplication operations not used in pure Python without third-party libraries?

In pure Python, the standard multiplication operations (*) are not intended for matrix multiplication, but work with numbers, strings, lists, etc. There is no built-in matrix multiplication operator because:

• Lack of specialized data types: the standard Python list is just a sequence of elements, not optimized for mathematical operations with matrices.
• Performance: matrix multiplication is computationally expensive, requiring optimizations that are implemented in specialized libraries.
• Operation semantics: the * operator for lists in Python means repetition, not element-wise multiplication.

Therefore, for working with matrices, third-party libraries like NumPy are used, which provide data types like ndarray and implement efficient matrix multiplication operations.

Example with NumPy:

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])

C = np.dot(A, B)  # or A @ B
print(C)

This is much more efficient and convenient than trying to implement matrix multiplication manually in pure Python.