How (and why) to raise e to the power of a matrix | DE6
General exponentials, Love, Schrödinger, and more.
Home page: https://www.3blue1brown.com
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The Romeo-Juliet example is based on this essay by Steven Strogatz:
http://www.stevenstrogatz.com/essays/loves-me-loves-me-not-do-the-math
The book shown at the start is Vladimir Arnold's (excellent) textbook on ordinary differential equations.
https://amzn.to/3dtXSwj
Need a review of ordinary powers of e?
https://youtu.be/m2MIpDrF7Es
Or of linear algebra?
https://youtu.be/kYB8IZa5AuE
Timetable
0:00 - Definition
6:40 - Dynamics of love
13:17 - General equation
20:03 - On general rotations
22:11 - Visualizing with flow
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Code for this video:
https://github.com/3b1b/videos/blob/master/_2021/matrix_exp.py
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https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
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https://github.com/3b1b/videos/
Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
Download the music on Bandcamp:
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Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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3Blue1Brown
3blue1brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective. Contact and F...