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:
Brought to you by you:

The Romeo-Juliet example is based on this essay by Steven Strogatz:

The book shown at the start is Vladimir Arnold’s (excellent) textbook on ordinary differential equations.

Need a review of ordinary powers of e?

Or of linear algebra?

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:

These animations made using a custom python library, manim. See the FAQ comments here:

You can find code for specific videos and projects here:

Music by Vincent Rubinetti.

Download the music on Bandcamp:

Stream the music on Spotify:


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:

Various social media stuffs:


Related post