In this video we introduce and prove the Riesz representation theorem for Hilbert spaces. This is the fundamental theorem that enables much of machine learning and data science, since it allows us to embed information and measurements from the real world into a Hilbert function space.
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The Real Analysis Survival Guide https://youtu.be/v5rD0B-zfXw
The Analyticity of the Laplace transform https://youtu.be/FIMkbFQL6XM
Introduction to Control Theory https://youtu.be/0v4WFmOm764
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0:00 What are functionals?
2:54 Functionals over R^n
3:55 Who proved this theorem?
5:00 Recapping the Projection Theorem
6:09 How do you prove this anyway?
16:25 Wrapping up