Norm
Also: L2 norm, Euclidean norm, L1 norm, vector norm
A function ‖v‖ that is zero only for the zero vector, scales with the vector and obeys the triangle inequality. The L2 norm is √(Σ vᵢ²); the L1 norm is Σ |vᵢ|. Norms define distances and regularization penalties.
‖v‖₂ = √(Σᵢ vᵢ²) ‖v‖₁ = Σᵢ |vᵢ|
Example
For v = (3, 4): the L2 norm is √(9 + 16) = 5 and the L1 norm is 3 + 4 = 7. Dividing by 5 gives the unit vector (0.6, 0.8).