Vectors

A vector is a 1-D array of numbers with magnitude and direction.

Vectors

A vector is an ordered list of numbers. In ML each example is a feature vector: [height, weight, age]. In NumPy it is a one-dimensional array; addition and scalar multiplication are element-wise:

u = np.array([1, 2, 3])
v = np.array([4, 5, 6])
print(u + v)       # [5 7 9]
print(2 * u)       # [2 4 6]

The length (norm) of a vector is found with np.linalg.norm(u): √(1² + 2² + 3²) ≈ 3.742.

Dot product

The dot product of two vectors is the sum of the products of corresponding elements. That is exactly a linear model's prediction: weights · features + intercept.

w = np.array([0.5, 2.0])
x = np.array([4, 3])
print(np.dot(w, x))   # 0.5*4 + 2.0*3 = 8.0
print(w @ x)          # the same

The dot product also measures how much two vectors point the same way; for perpendicular vectors the result is 0.

Exercise Linear prediction

The weight vector w, feature vector x and intercept b are given. Compute the prediction with w @ x + b and print it.

Show example solution

import numpy as np

w = np.array([2.0, -1.0, 0.5])
x = np.array([3, 4, 10])
b = 1.5

print(w @ x + b)

Test yourself

What is <code>np.linalg.norm([3, 4])</code>?
- 5.0
- 7.0
- 25.0
- 12.0
Show answer

5.0 — ��(3² + 4²) = √25 = 5.
Take the dot product of the two vectors.
```
skor = np.____(w, x)
```
Show answer
```
skor = np.dot(w, x)
```
Match the operations (u = [1, 2], v = [3, 4]).

u + v

[4 6]
u * v

[3 8]
u @ v

11
2 * u

[2 4]

Next lesson: Matrices

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