Properties and Uses of Norms

Linear Algebra for Machine Learning · Axiom Academy

Practice with different vectors and norm types Find the L2 norm of v = [3, -4] Using the Euclidean distance formula: ||v||₂ = 5. This is a unit-free magnitude—the "length" of the vector. Find the L1 norm of the same vector v = [3, -4] ||v||₁ = 7. The L1 norm is larger in this case, but that's specific to these numbers. Find the L∞ norm of v = [3, -4] ||v||∞ = 4. The maximum absolute value dominates. What is ||u||₂ for u = [1, 1, 1]? For any vector v with n components, which relationship is always true?

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