Vector Norm
A function assigning a non-negative size to a vector, generalizing length.
- Three axioms: positive-definite, homogeneous, triangle inequality.
- Common: L1 (Manhattan), L2 (Euclidean), L∞ (max).
- Choice of norm shapes regularization behavior.
When to use: Picking a regularizer (L1 for sparsity, L2 for smoothness) or distance metric.
Example: v = [3, -4, 0]: L1 = 7, L2 = 5, L∞ = 4.