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# Vectors, what even are they? | Essence of linear algebra, chapter 1

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## Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2

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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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

## Essence of linear algebra preview

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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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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## Linear transformations and matrices | Essence of linear algebra, chapter 3

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.

## Matrix multiplication as composition | Essence of linear algebra, chapter 4

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

## The determinant | Essence of linear algebra, chapter 6

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

## Dot products and duality | Essence of linear algebra, chapter 9

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

## Change of basis | Essence of linear algebra, chapter 12

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

## Eigenvectors and eigenvalues | Essence of linear algebra, chapter 13

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