Inner product spaces are objects which live at the intersection of algebra and geometry, adding interesting (and natural) geometry to the well known vector spaces. These inner product spaces have many applications both in mathematics and in general. They appear in probability, combinatorics, number theory, algorithms, data science, machine learning, physics and many more. Probably one of the most well known application is the famous Fourier transformations.
In these lectures we learn what are these inner product spaces, what are their properties and relations between different spaces, and how to use these inner products in many interesting and important applications.
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The video playlist on youtube.
| 0. Introduction and course format | video | |
| 1. Motivation: Dynamical systems Extra resources: *  matrix dynamics* Random walk dynamics | video | |
| 2. The inner product: From intuition to definition | video | |
| 3. The inner product: Basic properties | video | |
| 4. The norm | video | |
| 5. The triangle inequality | video | |
| In construction … |
Ofir David 