Inner product spaces – Youtube lectures (Hebrew)

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, 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.

Have any feedback on the course? I would love to hear about it.

The video playlist on youtube.

0. Introduction and motivation
Extra resources:
* 2\times 2 matrix dynamics
* Random walk dynamics		videonotes
1. Inner product spaces definitionvideonotes
2. Normsvideonotes
3. Unit balls
Extra resources:
* Unit balls in 2D (In geogebra)
* Unit balls in 3D (requires GPU)		videonotes
4. Perpendicular vectorsvideonotes
5. The Gram Schmidt processvideonotes
6. Distance from subspacevideonotes
7. Orthonormal basis
Extra resources:
* Approx f(x)=x by sine waves (geogebra)
* Orthonormal basis in 3D texturing (Hebrew video)		videonotes
8. Inner products and probabilityvideonotes
9. Programming – orthonormal setsvideopython notebook
10. Inner products and graphsvideonotes
11. Functionalsvideonotes
12. Adjoint Operatorvideonotes
13. Isometriesvideonotes (soon)
14. Reflections and rotationsvideonotes (soon)
15. The pseudoinverse and the least squares methodvideopython notebook
In construction …