Matrix multiplication with @ operator in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the @ operator do in numpy?

The @ operator performs matrix multiplication between two numpy arrays. It multiplies rows of the first matrix by columns of the second matrix and sums the products.

beginner

How is matrix multiplication different from element-wise multiplication?

Matrix multiplication combines rows and columns to produce a new matrix, while element-wise multiplication multiplies corresponding elements directly without combining rows and columns.

intermediate

Given two matrices A of shape (2, 3) and B of shape (3, 4), what will be the shape of A @ B?

The result will have shape (2, 4) because the inner dimensions (3) match and the output shape is the outer dimensions (2 from A and 4 from B).

intermediate

What error occurs if you try to multiply matrices with incompatible shapes using @?

You get a ValueError saying shapes are not aligned because the number of columns in the first matrix must equal the number of rows in the second matrix.

beginner

Write a simple numpy code snippet to multiply two matrices A and B using the @ operator.

import numpy as np
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
result = A @ B
print(result)

What does the @ operator do in numpy?

A Adds two matrices

B Performs element-wise multiplication

C Subtracts two matrices

D Performs matrix multiplication

The @ operator is used for matrix multiplication in numpy.

If matrix A has shape (3, 2) and matrix B has shape (2, 4), what is the shape of A @ B?

A (2, 2)

B (3, 4)

C (3, 2)

D (4, 3)

The output shape is (3, 4) because the inner dimensions 2 match and outer dimensions are 3 and 4.

What happens if you try to multiply matrices with shapes (2, 3) and (2, 4) using @?

A It works and returns shape (2, 4)

B It returns a scalar

C It raises a ValueError due to shape mismatch

D It performs element-wise multiplication

Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second matrix.

Which numpy function is equivalent to using the @ operator?

A np.dot()

B np.multiply()

C np.add()

D np.cross()

np.dot() performs matrix multiplication, same as the @ operator.

What is the result of multiplying a (2, 2) identity matrix with another (2, 2) matrix using @?

A The other matrix unchanged

B A zero matrix

C A matrix of ones

D An error

Multiplying by the identity matrix returns the other matrix unchanged.

Explain how the @ operator works for matrix multiplication in numpy.

Think about how you multiply matrices by hand.

Describe what happens if you try to multiply two numpy arrays with incompatible shapes using the @ operator.

Consider the rules for matrix multiplication dimensions.