How to multiply matrices with NumPy

Matrix multiplication combines rows and columns into weighted totals, which makes it a core operation in coordinate transforms, linear models, and equation systems. NumPy performs this calculation directly on regular arrays without manual nested loops.

For two-dimensional arrays, the left matrix shape (n, k) and right matrix shape (k, m) produce a result shaped (n, m). The shared inner dimension must match because each left row is paired with every right column.

The @ operator is the clearest form for two-dimensional matrix products and has the same semantics as np.matmul(). Keep * and np.multiply() for element-wise multiplication, and use ordinary ndarray values because the older numpy.matrix class is no longer recommended.

1. Create matrix-multiply.py with NumPy and two compatible operand arrays.

   matrix-multiply.py

   import numpy as np
    
   left = np.array(
       [
           [2, 1, 3],
           [0, 4, 5],
       ]
   )
   right = np.array(
       [
           [1, 2],
           [3, 0],
           [4, 1],
       ]
   )

   The left matrix has three columns and the right matrix has three rows, so their shared inner dimension is compatible.

2. Insert an inner-dimension check below the right array definition.

   if left.shape[1] != right.shape[0]:
       message = (
           f"left shape {left.shape} is incompatible "
           f"with right shape {right.shape}"
       )
       raise ValueError(message)

   This check reports the actual shapes before @ raises a lower-level dimension error, which is helpful when operands come from files or earlier transforms.

3. Append the matrix product and expected-result checks to matrix-multiply.py.

   product = left @ right
   expected = np.array(
       [
           [17, 7],
           [32, 5],
       ]
   )
    
   np.testing.assert_array_equal(product, expected)
   assert product.shape == (2, 2)
    
   print("product:")
   print(product)
   print("shape:", product.shape)
   print("matches expected:", np.array_equal(product, expected))

4. Run the completed matrix multiplication script.

   $ python3 matrix-multiply.py
   product:
   [[17  7]
    [32  5]]
   shape: (2, 2)
   matches expected: True

   The command exits with an assertion error if either the values or the (2, 2) result shape differs from the expected matrix.