MIT OpenCourseWare · Gilbert Strang · Fall 2011 (Scholar)

Linear Algebra, taught from the board.

All 32 lectures of 18.06SC rebuilt as structured lessons — Strang's own words, reorganized for reading, with every equation typeset, his best remarks pulled out, problems to work, and the four exams with solutions. Watch, read, work, tick it off.

Start with Session 01 Course on OCW ↗ Search the course
Unit 1

Ax = b and the Four Subspaces

  1. 01 The Geometry of Linear Equations
  2. 02 Elimination with Matrices
  3. 03 Multiplication and Inverse Matrices
  4. 04 Factorization into A = LU
  5. 05 Transposes, Permutations, Vector Spaces
  6. 06 Column Space and Nullspace
  7. 07 Solving Ax = 0: Pivot Variables, Special Solutions
  8. 08 Solving Ax = b: Row Reduced Form R
  9. 09 Independence, Basis, and Dimension
  10. 10 The Four Fundamental Subspaces
  11. 11 Matrix Spaces; Rank 1; Small World Graphs
  12. 12 Graphs, Networks, Incidence Matrices
  13. 13 An Overview of Key Ideas
  14. ★ Exam 1
Unit 2

Least Squares, Determinants and Eigenvalues

  1. 14 Orthogonal Vectors and Subspaces
  2. 15 Projections onto Subspaces
  3. 16 Projection Matrices and Least Squares
  4. 17 Orthogonal Matrices and Gram-Schmidt
  5. 18 Properties of Determinants
  6. 19 Determinant Formulas and Cofactors
  7. 20 Cramer's Rule, Inverse Matrix, and Volume
  8. 21 Eigenvalues and Eigenvectors
  9. 22 Diagonalization and Powers of A
  10. 23 Differential Equations and exp(At)
  11. 24 Markov Matrices; Fourier Series
  12. ★ Exam 2
Unit 3

Positive Definite Matrices and Applications

  1. 25 Symmetric Matrices and Positive Definiteness
  2. 26 Complex Matrices; Fast Fourier Transform
  3. 27 Positive Definite Matrices and Minima
  4. 28 Similar Matrices and Jordan Form
  5. 29 Singular Value Decomposition
  6. 30 Linear Transformations and Their Matrices
  7. 31 Change of Basis; Image Compression
  8. 32 Left and Right Inverses; Pseudoinverse
  9. ★ Exam 3
  10. ★ Final Exam

Content derives from MIT OCW 18.06SC (Prof. Gilbert Strang), CC BY-NC-SA 4.0. Lecture videos © MIT OpenCourseWare.