3Blue1Brown Series
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Play S1 E13Blue1Brown is a channel about animating math, in all senses of the word animate.
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16 episodes
1. Vectors, what even are they?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.CCAug 6, 2016
2. Linear combinations, span, and basis vectorsThe 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.CCAug 7, 2016
3. Linear transformations and matricesMatrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra.CCAug 7, 2016
4. Matrix multiplication as compositionMultiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact.CCAug 9, 2016
5. Three-dimensional linear transformationsWhat 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.CCAug 10, 2016
6. The determinantThe determinant of a linear transformation measures how much areas/volumes change during the transformation.CCAug 11, 2016
7. Inverse matrices, column space and null spaceHow 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.CCAug 16, 2016
8. Nonsquare matrices as transformations between dimensionsBecause people asked, this is a video briefly showing the geometric interpretation of non-square matrices as linear transformations that go between dimensions.CCAug 16, 2016
9. Dot products and dualityDot 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.CCAug 24, 2016
10. Cross productsThis covers the main geometric intuition behind the 2d and 3d cross products.CCSep 1, 2016
11. Cross products in the light of linear transformationsFor 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.CCSep 3, 2016
12. Cramer's rule, explained geometricallyThis rule seems random to many students, but it has a beautiful reason for being true.CCMar 17, 2019
13. Change of basisHow do you translate back and forth between coordinate systems that use different basis vectors?CCSep 11, 2016
14. Eigenvectors and eigenvaluesA visual understanding of eigenvectors, eigenvalues, and the usefulness of an eigenbasis.CCSep 15, 2016
15. A quick trick for computing eigenvaluesHow to write the eigenvalues of a 2x2 matrix just by looking at it.CC13minMay 7, 2021
16. Abstract vector spacesThis is really the reason linear algebra is so powerful.CC17minSep 24, 2016
3Blue1Brown Series
★ 9.0/1020164 seasons38 episodesReturning Series
3Blue1Brown is a channel about animating math, in all senses of the word animate.
Creators and cast
- Directors
- Grant Sanderson
- Created by
- Grant Sanderson
Maturity rating
Not yet rated.
Audio languages
English
Where to watch
Not currently listed on any streaming, rental or purchase service.
Details and artwork from TMDB. Availability from JustWatch and can change without notice.