Matrix multiplication
- Machine Learning course
- Beginner
- Lesson 33/112
- 5 min
Matrix multiplication is done with np.dot() or the @ operator.
Matrix multiplication
Multiplying A of shape (m, n) by B of shape (n, p) gives a matrix of shape (m, p). Each element of the result is the dot product of a row of A and a column of B.
A = np.array([[1, 2],
[3, 4]])
B = np.array([[5, 6],
[7, 8]])
print(A @ B) # [[19 22] [43 50]]
# 19 = 1*5 + 2*7A * B is element-wise multiplication and gives a completely different result: [[5 12] [21 32]].
Batch prediction
Matrix multiplication gives the predictions for all examples in one operation. In a linear model you write X @ w + b, in a neural network layer X @ W + b:
X = np.array([[1, 2],
[3, 4],
[5, 6]]) # 3 examples, 2 features
w = np.array([0.5, 1.0])
print(X @ w + 1) # [3.5 6.5 9.5]The speed of deep learning comes from GPUs being able to do these multiplications highly in parallel.
Practice Predict all examples
Compute all predictions with X @ w + b from X (4 examples, 2 features) and w. Print the predictions and their shape.
Starter code
import numpy as np
X = np.array([[1, 1], [2, 0], [0, 3], [4, 2]])
w = np.array([3, -2])
b = 5
# buraya yazSample solution
import numpy as np
X = np.array([[1, 1], [2, 0], [0, 3], [4, 2]])
w = np.array([3, -2])
b = 5
tahmin = X @ w + b
print(tahmin)
print(tahmin.shape)Expected output
[ 6 11 -1 13] (4,)
Questions and answers
Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.
1 If X of shape (4, 3) is multiplied by W of shape (3, 2), what is the shape of <code>X @ W</code>?
- (4, 3)
- An error
- (4, 2) Correct answer
- (3, 3)
Explanation: The inner dimensions (3) match and disappear; the outer ones (4, 2) remain.
2 Do the matrix multiplication.
C = A ____ BC = A @ BExplanation: @ is matrix multiplication; * is element-wise.
3 Match the shapes.
| Term | Meaning |
|---|---|
(2, 3) @ (3, 4) |
(2, 4) |
(5, 2) @ (2,) |
(5,) |
(3, 3) @ (3, 1) |
(3, 1) |
(2, 3) @ (2, 3) |
Error |