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3Blue1Brown Series Episode Guide
Vectors, what even are they?
S1 Ep1
6th Aug 2016
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.
Linear combinations, span, and basis vectors
S1 Ep2
7th Aug 2016
The fundamental vector concepts of span, linear combinations, linear dependence, and bases all center on one surprisingly important operation: Scaling several vectors and adding them together.
Linear transformations and matrices
S1 Ep3
7th Aug 2016
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
S1 Ep4
9th Aug 2016
Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact.
Three-dimensional linear transformations
S1 Ep5
10th Aug 2016
What do 3d linear transformations look like? Having talked about the relationship between matrices and transformations in the last two videos, this one extends those same concepts to three dimensions.
The determinant
S1 Ep6
11th Aug 2016
The determinant of a linear transformation measures how much areas/volumes change during the transformation.
Inverse matrices, column space and null space
S1 Ep7
16th Aug 2016
How to think about linear systems of equations geometrically. The focus here is on gaining an intuition for the concepts of inverse matrices, column space, rank and null space, but the computation of those constructs is not discussed.
Nonsquare matrices as transformations between dimensions
S1 Ep8
16th Aug 2016
Because people asked, this is a video briefly showing the geometric interpretation of non-square matrices as linear transformations that go between dimensions.
Dot products and duality
S1 Ep9
24th Aug 2016
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 going on with the dot product, and the connection between its numerical computation and its geometric interpretation.
Cross products
S1 Ep10
1st Sep 2016
This covers the main geometric intuition behind the 2d and 3d cross products.
Cross products in the light of linear transformations
S1 Ep11
3rd Sep 2016
For anyone who wants to understand the cross product more deeply, this video shows how it relates to a certain linear transformation via duality. This perspective gives a very elegant explanation of why the traditional computation of a dot product corresponds to its geometric interpretation.
Cramer's rule, explained geometrically
S1 Ep12
17th Mar 2019
This rule seems random to many students, but it has a beautiful reason for being true.
Change of basis
S1 Ep13
11th Sep 2016
How do you translate back and forth between coordinate systems that use different basis vectors?
Eigenvectors and eigenvalues
S1 Ep14
15th Sep 2016
A visual understanding of eigenvectors, eigenvalues, and the usefulness of an eigenbasis.
A quick trick for computing eigenvalues
S1 Ep15
7th May 2021
How to write the eigenvalues of a 2x2 matrix just by looking at it.
Abstract vector spaces
S1 Ep16
24th Sep 2016
This is really the reason linear algebra is so powerful.
3Blue1Brown is a channel about animating math, in all senses of the word animate.
The first episode of 3Blue1Brown Series aired on August 06, 2016.
The last episode of 3Blue1Brown Series aired on May 07, 2021.
There are 38 episodes of 3Blue1Brown Series.
There are 4 seasons of 3Blue1Brown Series.
Yes.
3Blue1Brown Series is set to return for future episodes.
