Norm measures the magnitude of a vector.
Norm needs to satisfy the following properties:
- Positivity:
- triangle inequality:
Even though we usually talks about L2 norm, there are a lot of different kind of norms that satisfy the above 4 properties. For example, L1 norm and infinity norm are other example of a norm. We can generalize the
The Cauchy-Schwarz inequality describes the relationship between norm and inner product.