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Kicking off the linear algebra lessons, let's make sure we're all on the same page about how specifically to think about vectors in this context. Typo correction: At 6:52, the screen shows [x1, y1] + [x2, y2] = [x1+y1, x2+y2]. Of course, this should actually be [x1, y1] + [x2, y2] = [x1+x1, y2+y2]. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. Music: https://vincerubinetti.bandcamp.com/track/grants-etude ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown

The fundamental vector concepts of span, linear combinations, linear dependence, and bases all center on one surprisingly important operation: Scaling several v

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Bobby Fischer creates a chess masterpiece in only 21 moves against Robert Eugene Byrne, an International Master, at the 1963/1964 United States Chess Championsh

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Before we get into non-Euclidian geometry, we have to know: what even is geometry? What's up with the Pythagorean math cult? Who was Euclid, for that matter? An

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Two lovely ways of relating a sphere's surface area to a circle. Fourier socks, pi plushies, and more: http://3b1b.co/store Happy holidays! Discuss on reddit:

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An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery a

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This introduces the "Essence of linear algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear al

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I want you to feel that you could have invented calculus for yourself, and in this first video of the series, we see how unraveling the nuances of a simple geom

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Featuring Matt Parker... Part 2 (solution) here: https://youtu.be/pasyRUj7UwM More links & stuff in full description below ↓↓↓ Discuss this video on Brady's su

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What is e? And why are exponentials proportional to their own derivatives? Full series: http://3b1b.co/calculus Series like this one are funded largely by the

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Intuitions for divergence and curl, and where they come up in physics. Thoughts on going sponsor-free: https://www.patreon.com/posts/19586800 Special thanks to

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In math, exponents, logarithms, and roots all circle around the same idea, but the notation for each varies radically. The triangle of power is an alternate no

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Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra.

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Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this

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The determinant of a linear transformation measures how much areas/volumes change during the transformation. Full series: http://3b1b.co/eola Future series li

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Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's goi

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How do you translate back and forth between coordinate systems that use different basis vectors? Full series: http://3b1b.co/eola Future series like this are

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A visual understanding of eigenvectors, eigenvalues, and the usefulness of an eigenbasis. Full series: http://3b1b.co/eola Future series like this are funded

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The tools of linear algebra are extremely general, applying not just to the familiar vectors that we picture as arrows in space, but to all sorts of mathematica

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