How (and why) to raise e to the power of a matrix | DE6

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Genre: Education

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3Blue1Brown

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Shared April 1, 2021

General exponentials, love, Schrödinger, and more.
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The Romeo-Juliet example is based on this essay by Steven Strogatz:
http://www.stevenstrogatz.com/essays/...

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​ - Linear systems
20:03​ - General rotations
22:11​ - Visualizing with flow

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Code for this video:
https://github.com/3b1b/videos/blob/m...

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https://github.com/3b1b/manim

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Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/

Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/a...

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...

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