Books

MIT OpenCourseWare

Browse materialsMIT 18.06SC · Fall 2011

Linear Algebra

Subjects: Algebra · Linear Algebra · Mathematics

Art: Anonymous painter,15th century, Westerner and Arab practicing geometry 15th century manuscript, 15th… · Public domain

Instructor
Prof. Gilbert Strang
Term
Fall 2011
Level
Undergraduate
What's inside
158 videos · 7 exams · 1 solution · 266 other files · 41 web pages
Materials open
Videos here · files on MIT OCW
Other versions of this course

Start here

Start course: Linear Algebra Course IntroductionFind a topic

Progress is saved in this browser.

Export or import progress
About this course

Source: MIT OpenCourseWare 18.06SC Linear Algebra, Fall 2011, Prof. Gilbert Strang — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 22, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Study loop: The Geometry of Linear Equations

MIT's session page places these resources together. RedLectern's suggested study order: Watch → Read → Attempt → Check → Continue.

  1. Watch · The Geometry of Linear Equations MIT resource
  2. Read · Lecture summary (PDF) MIT resource
  3. Attempt · Problems (PDF) MIT resource
  4. Check · MIT resource
  5. Continue · Elimination with Matrices

Study loop: Elimination with Matrices

MIT's session page places these resources together. RedLectern's suggested study order: Watch → Read → Attempt → Check → Continue.

  1. Watch · Elimination with Matrices MIT resource
  2. Read · Lecture summary (PDF) MIT resource
  3. Attempt · Problems (PDF) MIT resource
  4. Check · MIT resource
  5. Continue · Factorization into A = LU

Learn one topic

32 concept pages, one per MIT session: the clips, notes and practice for that topic. MIT solutions for 31 of 32 topics.

All 32 topics
  1. The Geometry of Linear Equations MIT solutions
  2. An Overview of Key Ideas
  3. Elimination with Matrices MIT solutions
  4. Multiplication and Inverse Matrices MIT solutions
  5. Factorization into A = LU MIT solutions
  6. Transposes, Permutations, Vector Spaces MIT solutions
  7. Column Space and Nullspace MIT solutions
  8. Solving Ax = 0: Pivot Variables, Special Solutions MIT solutions
  9. Solving Ax = b: Row Reduced Form R MIT solutions
  10. Independence, Basis and Dimension MIT solutions
  11. The Four Fundamental Subspaces MIT solutions
  12. Matrix Spaces; Rank 1; Small World Graphs MIT solutions
  13. Graphs, Networks, Incidence Matrices MIT solutions
  14. Orthogonal Vectors and Subspaces MIT solutions
  15. Projections onto Subspaces MIT solutions
  16. Projection Matrices and Least Squares MIT solutions
  17. Orthogonal Matrices and Gram-Schmidt MIT solutions
  18. Properties of Determinants MIT solutions
  19. Determinant Formulas and Cofactors MIT solutions
  20. Cramer's Rule, Inverse Matrix and Volume MIT solutions
  21. Eigenvalues and Eigenvectors MIT solutions
  22. Diagonalization and Powers of A MIT solutions
  23. Differential Equations and exp(At) MIT solutions
  24. Markov Matrices; Fourier Series MIT solutions
  25. Symmetric Matrices and Positive Definiteness MIT solutions
  26. Complex Matrices; Fast Fourier Transform (FFT) MIT solutions
  27. Positive Definite Matrices and Minima MIT solutions
  28. Similar Matrices and Jordan Form MIT solutions
  29. Singular Value Decomposition MIT solutions
  30. Linear Transformations and their Matrices MIT solutions
  31. Change of Basis; Image Compression MIT solutions
  32. Left and Right Inverses; Pseudoinverse MIT solutions

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Introduction to Linear Algebra · Differential Equations and Linear Algebra · Linear Algebra and Learning from Data

How this course was organized

What's here, and what isn't

  • This course has 78 videos, each embedded on its own MIT page, across 38 sections. They're shown in MIT's listing order within each section. A verified course-wide order is not claimed for this course.

Not included here

20 items from the source could not be safely included:

  • MIT's page format for this item wasn't recognized clearly enough to place it safely. (12 items)
  • Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (8 items)

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Instructor Insights

Unit I: Ax = b and the Four Subspaces

81 items in this section

The Geometry of Linear Equations

3 files

2 videos

2 video transcripts

An Overview of Key Ideas

Elimination with Matrices

Multiplication and Inverse Matrices

Factorization into A = LU

Transposes, Permutations, Vector Spaces

3 files

2 videos

2 video transcripts

Column Space and Nullspace

Solving Ax = 0: Pivot Variables, Special Solutions

Solving Ax = b: Row Reduced Form R

Independence, Basis and Dimension

The Four Fundamental Subspaces

Matrix Spaces; Rank 1; Small World Graphs

Graphs, Networks, Incidence Matrices

Exam 1 Review

Exam 1

Unit II: Least Squares, Determinants and Eigenvalues

65 items in this section

Orthogonal Vectors and Subspaces

Projections onto Subspaces

Projection Matrices and Least Squares

Orthogonal Matrices and Gram-Schmidt

Properties of Determinants

Determinant Formulas and Cofactors

Cramer's Rule, Inverse Matrix and Volume

Eigenvalues and Eigenvectors

Diagonalization and Powers of A

Differential Equations and exp(At)

Markov Matrices; Fourier Series

Exam 2 Review

Exam 2

Unit III: Positive Definite Matrices and Applications

51 items in this section

Symmetric Matrices and Positive Definiteness

Complex Matrices; Fast Fourier Transform (FFT)

Positive Definite Matrices and Minima

Similar Matrices and Jordan Form

Singular Value Decomposition

Linear Transformations and their Matrices

Change of Basis; Image Compression

Left and Right Inverses; Pseudoinverse

Exam 3 Review

Exam 3

Final Course Review

Final 18.06 Lecture 2023

Resource Index

3 files

52 videos

Other materials from this course

14 files
75 video transcripts
52 images

MIT OpenCourseWare, Prof. Gilbert Strang, 18.06SC Linear Algebra, Fall 2011.

License: CC BY-NC-SA 4.0 · Edition: Fall 2011 · Open the original course on OCW ↗

Organized by RedLectern, independent of MIT and not endorsed by MIT.

Per-resource rights are recorded on each resource; All-Rights-Reserved items are link-only, never mirrored.