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Explore How (and why) to raise e to the power of a matrix | DE6 with 3,639,541 views, 89,515 likes, and 3,060 comments. Experience the impact of this video content that has captured audience attention.

General exponentials, love, Schrödinger, and more. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/mat-exp-thanks Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 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

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