# Cauchy-Schwarz Inequality

##### 61 words — categories: linear-algebra

The **Cauchy-Schwarz inequality** states for all vectors \(u\) and \(v\),

\[|\langle \mathbf{u}, \mathbf{v} \rangle| \leq ||\mathbf{u}|| \ ||\mathbf{v}||\]

This means that the dot product of the two vectors is less than the product of the norms of the vectors.

```
import numpy as np
u = np.array([3, 5, 5])
v = np.array([5, 2, 6])
np.dot(u, v) <= np.linalg.norm(u) * np.linalg.norm(v)
```

`## True`