How (and why) to raise e to the power of a matrix | DE6
General exponentials, love, Schrödinger, and more.
Enjoy these videos? Consider sharing one or two.
Supported by viewers: https://3b1b.co/mat-exp-thanks
------------------
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 - Linear systems
20:03 - General rotations
22:11 - Visualizing with flow
------------------
Code for this video:
https://github.com/3b1b/videos/blob/master/_2021/matrix_exp.py
These animations made using a custom python library, manim. See the FAQ comments here:
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:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Видео How (and why) to raise e to the power of a matrix | DE6 канала 3Blue1Brown
Enjoy these videos? Consider sharing one or two.
Supported by viewers: https://3b1b.co/mat-exp-thanks
------------------
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 - Linear systems
20:03 - General rotations
22:11 - Visualizing with flow
------------------
Code for this video:
https://github.com/3b1b/videos/blob/master/_2021/matrix_exp.py
These animations made using a custom python library, manim. See the FAQ comments here:
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:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Видео How (and why) to raise e to the power of a matrix | DE6 канала 3Blue1Brown
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