Norm #
A norm measures the length (magnitude) of a vector.
- the norm of a vector x measures the distance from the origin to the point x.
Common example: Euclidean norm.
\[ \lVert \mathbf{x} \rVert_2 = \sqrt{x_1^2 + \cdots + x_n^2} \]Common norms #
- L1
- L2
- Infinity norm
Why it matters #
- norms quantify size
- are used in distances and regularisation.