Linear Algebra · L3 Code

Implementing dot products, matrix multiplies, and a linear layer from scratch with NumPy, then verifying against PyTorch.

By hand (loops)

Triple nested for-loop
Correct but painfully slow
Good for building intuition

Vectorized (NumPy/PyTorch)

Single @ operator call
Runs on optimized BLAS/GPU kernels
What real code always uses

python

import numpy as np

def dot(x, y):
    total = 0.0
    for xi, yi in zip(x, y):
        total += xi * yi
    return total

def matmul_naive(A, B):
    m, n = A.shape
    n2, p = B.shape
    assert n == n2, "inner dimensions must match"
    C = np.zeros((m, p))
    for i in range(m):
        for j in range(p):
            C[i, j] = dot(A[i, :], B[:, j])
    return C

A = np.random.randn(4, 3)
B = np.random.randn(3, 2)
print(np.allclose(matmul_naive(A, B), A @ B))  # True

A dot product and a naive matrix multiply, written with explicit loops.