Proof: All Norms Are Convex
Professor of Mechanical Engineering
18:51·2026·graduate level·Standalone Lecture
Professor Steve Brunton proves the convexity of all norms, discussing its fundamental implications for optimization theory and machine learning algorithms.
Theory & AlgosMathematicsAlgorithms & Data StructuresLinear AlgebraConvex Optimizationfunctional analysis
This lecture proves that all norms are convex and discusses the implications of norm complexity for optimization, especially in machine learning.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company.
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