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Miniatures: Mathematical and Algorithmic Applications of Linear Algebra [pdf] (cuni.cz)
247 points by vinchuco 217 days ago | hide | past | web | 11 comments | favorite



Essence of linear algebra [1] , in 3blue1brown youtube channel totally changed my perspective on Linear Algebra. One of the best channels in YouTube I have seen so far. He makes his videos using the animation engine [2] he built himself.

[1] https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...

[2] https://github.com/3b1b/manim


That whole channel is amazing! I can start just listing all the videos by virtue of picking out awesome ones, but check out the one he did on Euler's formula[1]. Blew my mind.

[1]https://www.youtube.com/watch?v=mvmuCPvRoWQ&t=385s


I didn't know pretty much anything about linear algebra, but by watching the series, I felt deep enlightenment. Also, the videos they have done about topology really made me believe everything is, in essence, geometry.


I like these! Work related to number 9 came up just three days ago: https://news.ycombinator.com/item?id=14114876


If you enjoy this, Matousek and Vondrak have a better one. http://webbuild.knu.ac.kr/~trj/Combin/matousek-vondrak-prob-...


>If you enjoy this, Matousek and Vondrak have a better one.

Curious as to why you would say that. Having a cursory look at both, they don't appear to be even close to discussing the same things. The link you provided is much more theoretical, and about probability.



example 12, "Tiling a Rectangle by Squares" is rather unique; it was discussed in Stanislav Smirnov's Fields medal lecture in 2010

https://en.wikipedia.org/wiki/Squaring_the_square

In his lecture he puts the square tilings in a rather serious context (the theory of electrical networks)

https://arxiv.org/abs/1009.6077 ( Discrete Complex Analysis and Probability )


I think the most amazing thing is that Linear Algebra works the same for any fields, not just R and C. Applying it to finite fields is a great trick.


And some of the familiar linear algebra theorems extend to infinite dimensional spaces. For instance spectral theory of compact operators [1]

[1] https://en.wikipedia.org/wiki/Spectral_theory_of_compact_ope...


Which of these miniatures is most relevant to CS or real-world software problems?




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