Lengths and Distances #
The length of a vector is given by its norm.
The distance between two points (vectors) is the norm of their difference.
Distance quantifies how far two vectors (data points) are from each other.
\[ d(\mathbf{x},\mathbf{y}) = \lVert \mathbf{x} - \mathbf{y} \rVert \]Why it matters #
- many ML algorithms depend on distances in feature space