Linear Algebra: A Geometric Introduction to Vectors, Matrices and Eigenvalues
A 16-part visual course that builds linear algebra from geometric intuition: vectors, span and basis, linear transformations, matrix multiplication, determinants, inverses, dot and cross products, change of basis, and eigenvectors. It ends with abstract vector spaces. It suits learners who want to understand why the formulas work, either before or alongside a conventional computational course.
Lessons by 3Blue1Brown on YouTubeCurated by YodaHut. These lessons are hosted on YouTube and produced by their original creators, who are not affiliated with YodaHut. You still earn YodaCoins, keep your streak and track progress here.
What You'll Learn
- Interpret vectors, linear combinations, span and basis vectors geometrically
- Read a matrix as a linear transformation and see matrix multiplication as composing transformations
- Explain the determinant as a change in area or volume, and relate inverses, rank, column space and null space to solving linear systems
- Understand dot and cross products through projection, duality and transformations, and see why Cramer's rule works
- Translate vectors and transformations between coordinate systems using change of basis
- Find and interpret eigenvectors and eigenvalues, including a shortcut for 2x2 matrices, and describe how vector spaces generalise beyond arrows
Prerequisites
- Comfortable with high-school algebra and coordinate geometry
- Basic trigonometry is helpful for the dot product and cross product lessons
Course Curriculum
- 1Vectors9:52
- 2Linear Combinations, Span, and Basis Vectors9:59
- 3Linear Transformations and Matrices10:59
- 4Matrix Multiplication as Composition10:04
- 5Three-Dimensional Linear Transformations4:46
- 6The Determinant10:03
- 7Inverse Matrices, Column Space and Null Space12:09
- 8Nonsquare Matrices as Transformations Between Dimensions4:27
- 9Dot Products and Duality14:12
- 10Cross Products8:54
- 11Cross Products in the Light of Linear Transformations13:10
- 12Cramer's Rule, Explained Geometrically12:12
- 13Change of Basis12:51
- 14Eigenvectors and Eigenvalues17:16
- 15A Quick Trick for Computing Eigenvalues13:13
- 16Abstract Vector Spaces16:46
About the Instructor
3Blue1Brown
YouTube creator
The lessons in this course were produced by 3Blue1Brown and are published on YouTube. YodaHut selected and sequenced them into this course; we did not make them, and 3Blue1Brown is not affiliated with YodaHut.
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- 16 lessons
- 3h 1m of video
- Earns YodaCoins & streaks
- Timestamped notes
- Free — hosted on YouTube
No certificate is issued for Library courses.