How to write the eigenvalues of a 2x2 matrix just by looking at it. Need a refresher on eigenvalues? https://youtu.be/PFDu9oVAE-g Thanks to Tim for the jingle: https://www.youtube.com/acapellascience Help fund future projects: https://www.patreon.com/3blue1brown​ An equally valuable form of support is to simply share the videos. Special thanks to these supporters: https://3b1b.co/quick-eigen-thanks

Lockdown math lecture talking about the mean product formula: https://youtu.be/MHXO86wKeDY

Timestamps: 0:00 - Background 4:53 - Examples 10:24 - Relation to the characteristic polynomial 12:00 - Last thoughts

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These animations are largely made using a custom python library, manim. See the FAQ comments here: https://www.3blue1brown.com/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/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

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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