Linear Algebra (MIT 18.06): Matrices, Vector Spaces, Eigenvalues and SVD
A complete university-level linear algebra course taught by Gilbert Strang. It goes from solving systems with elimination through vector spaces, orthogonality and least squares, determinants, eigenvalues, and on to the SVD, linear transformations and pseudoinverses. It suits students in science, engineering, data or math who are comfortable with basic algebra and want a rigorous, computation-first treatment.
Lessons by MIT OpenCourseWare 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
- Solve linear systems using elimination, LU factorization, inverses and row reduced form, and describe the solutions geometrically
- Work with column space, nullspace, independence, basis, dimension and the four fundamental subspaces of a matrix
- Compute projections, least-squares fits, orthogonal bases and Gram-Schmidt (QR) factorizations
- Calculate determinants with properties, cofactors and Cramer's rule, and interpret them as volumes
- Find eigenvalues and eigenvectors, diagonalize matrices, compute matrix powers and solve differential equations with exp(At)
- Apply symmetric and positive definite matrices, the SVD, Jordan form, change of basis and pseudoinverses
Prerequisites
- Solid high-school algebra
- Some familiarity with vectors and basic calculus helps for the differential equations and minima lectures, but is not essential
Course Curriculum
- 1Interview with Gilbert Strang on Teaching Linear Algebra7:34
- 2The Geometry of Linear Equations39:49
- 3Elimination with Matrices47:42
- 4Multiplication and Inverse Matrices46:49
- 5Factorization into A = LU48:05
- 6Transposes, Permutations, Spaces R^n47:42
- 7Column Space and Nullspace46:01
- 8Solving Ax = 0: Pivot Variables, Special Solutions43:20
- 9Solving Ax = b: Row Reduced Form R47:20
- 10Independence, Basis, and Dimension50:14
- 11The Four Fundamental Subspaces49:20
- 12Matrix Spaces; Rank 1; Small World Graphs45:56
- 13Graphs, Networks, Incidence Matrices47:57
- 14Quiz 1 Review47:40
- 15Orthogonal Vectors and Subspaces49:48
- 16Projections onto Subspaces48:51
- 17Projection Matrices and Least Squares48:05
- 18Orthogonal Matrices and Gram-Schmidt49:10
- 19Properties of Determinants49:12
- 20Determinant Formulas and Cofactors53:17
- 21Cramer's Rule, Inverse Matrix, and Volume51:01
- 22Eigenvalues and Eigenvectors51:23
- 23Diagonalization and Powers of A51:50
- 24Differential Equations and exp(At)51:03
- 25Markov Matrices; Fourier Series51:12
- 26Quiz 2 Review48:20
- 27Symmetric Matrices and Positive Definiteness43:52
- 28Complex Matrices; Fast Fourier Transform47:52
- 29Positive Definite Matrices and Minima50:40
- 30Similar Matrices and Jordan Form45:56
- 31Singular Value Decomposition40:29
- 32Linear Transformations and Their Matrices49:27
- 33Change of Basis; Image Compression50:14
- 34Quiz 3 Review47:06
- 35Left and Right Inverses; Pseudoinverse41:53
- 36Final Course Review43:26
About the Instructor
MIT OpenCourseWare
YouTube creator
The lessons in this course were produced by MIT OpenCourseWare and are published on YouTube. YodaHut selected and sequenced them into this course; we did not make them, and MIT OpenCourseWare is not affiliated with YodaHut.
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- 36 lessons
- 27h 60m of video
- Earns YodaCoins & streaks
- Timestamped notes
- Free — hosted on YouTube
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