Vector norm
A norm assigns a nonnegative size to a vector and satisfies definiteness, homogeneity, and the triangle inequality.
Definition
A norm assigns a nonnegative size to a vector and satisfies definiteness, homogeneity, and the triangle inequality.
Intuition
The choice of norm determines what counts as a large vector or error.
Worked example
For (3, 4), the L2 norm is 5 and the L1 norm is 7.
The math
and .
In machine learning
Norms measure residual error, regularize model weights, and normalize embeddings.
Go deeper
Sources
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