Essence of Linear Algebra (3Blue1Brown)
By 3Blue1Brown
- Course audio
- Course audio: English
- Level
- Intermediate
- Length
- 15 lessons
What you'll be able to do
- Picture vectors, span and basis geometrically
- Interpret matrices and determinants as transformations
- Understand eigenvectors and change of basis intuitively
About this course
Grant Sanderson's animated series that builds a geometric picture of linear algebra. Chapters cover vectors, linear combinations, span and basis, linear transformations as matrices, matrix multiplication as composition, determinants, inverse matrices and column space, dot and cross products, change of basis, and eigenvectors and eigenvalues. It suits FSc and university students who can do matrix arithmetic but want to see what it means, and it pairs well with a lecture course such as MIT 18.06 taken afterwards.
Before you start: FSc-level algebra; some exposure to matrices helps
Syllabus
Sabaq lists the first 15 videos of this playlist; the rest continue on YouTube. Full playlist on YouTube
- 1Vectors | Chapter 1, Essence of linear algebra
- 2Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra
- 3Linear transformations and matrices | Chapter 3, Essence of linear algebra
- 4Matrix multiplication as composition | Chapter 4, Essence of linear algebra
- 5Three-dimensional linear transformations | Chapter 5, Essence of linear algebra
- 6The determinant | Chapter 6, Essence of linear algebra
- 7Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra
- 8Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebra
- 9Dot products and duality | Chapter 9, Essence of linear algebra
- 10Cross products | Chapter 10, Essence of linear algebra
- 11Cross products in the light of linear transformations | Chapter 11, Essence of linear algebra
- 12Cramer's rule, explained geometrically | Chapter 12, Essence of linear algebra
- 13Change of basis | Chapter 13, Essence of linear algebra
- 14Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
- 15A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra
What to take next
Related courses
Videos by 3Blue1Brown, played from their official YouTube channel. Subscribe on YouTube
Official upload by the teacher or institution on their own channel, shown with YouTube's embedded player.
Sabaq lists the first 15 videos of this playlist; the rest continue on YouTube. Full playlist on YouTube
Lessons last checked Oct 2026. Course summary and lesson structure by Sabaq.
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