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

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
Brought to you by you: https://3b1b.co/mat-exp-thanks

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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?

Or of linear algebra?

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/master/_2021/matrix_exp.py

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https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim

You can find code for specific videos and projects here:
https://github.com/3b1b/videos/

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

Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:

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