MIT OpenCourseWare

Browse materialsMIT 18.06 · Spring 2010

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: Spring 2010
Level: Undergraduate
What's inside: 37 videos · 4 exams · 14 solutions · 1 reading · 77 other files · 9 web pages
Materials open: Videos here · files on MIT OCW

Other versions of this course

18.06SC+summer_2019 · Summer 2019 · On MIT OCW ↗
18.06SC · Fall 2011 · Study here
18.06 · Spring 2010 · Study here (this version)

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Start course: Lecture 1: The geometry of linear equations Find a topic

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About this course

Source: MIT OpenCourseWare 18.06 Linear Algebra, Spring 2010, 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.

Has MIT solutions 14 files in this course are named by MIT as 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 · Introduction to Linear Algebra · Introduction to Linear Algebra · Introduction to Linear Algebra

How this course was organized

What's here, and what isn't

MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.

Not included here

30 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. (28 items)
Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (2 items)

Materials by section

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

Instructor Insights

An Interview with Gilbert Strang on Teaching Linear AlgebraVideo Open ↗

Final 18.06 Lecture 2023

Gil Strang's Final 18.06 Linear Algebra LectureVideo Open ↗

Assignments

10 problem sets

Exams

8 files

Related Resources

Other materials from this course

35 lecture transcripts

37 video transcripts

41 images

MIT OpenCourseWare, Prof. Gilbert Strang, 18.06 Linear Algebra, Spring 2010.

License: CC BY-NC-SA 4.0 · Edition: Spring 2010 · Open the original course on OCW ↗

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

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Linear Algebra

Before you start

What's here, and what isn't

Not included here

Materials by section

Instructor Insights

Final 18.06 Lecture 2023

Assignments

Exams

Related Resources

Other materials from this course

Lecture 1: The geometry of linear equations

Lecture 2: Elimination with matrices

Lecture 3: Multiplication and inverse matrices

Lecture 4: Factorization into A = LU

Lecture 5: Transposes, permutations, spaces Rⁿ

Lecture 6: Column space and nullspace

Lecture 7: Solving Ax = 0: pivot variables, special solutions

Lecture 8: Solving Ax = b: row reduced form R

Lecture 9: Independence, basis, and dimension

Lecture 10: The four fundamental subspaces

Lecture 11: Matrix spaces; rank 1; small world graphs

Lecture 12: Graphs, networks, incidence matrices

Lecture 13: Quiz 1 review

Lecture 14: Orthogonal vectors and subspaces

Lecture 15: Projections onto subspaces

Lecture 16: Projection matrices and least squares

Lecture 17: Orthogonal matrices and Gram-Schmidt

Lecture 18: Properties of determinants

Lecture 19: Determinant formulas and cofactors

Lecture 20: Cramer's rule, inverse matrix, and volume

Lecture 21: Eigenvalues and eigenvectors

Lecture 22: Diagonalization and powers of A

Lecture 23: Differential equations and exp(At)

Lecture 24: Markov matrices; fourier series

Lecture 24b: Quiz 2 review

Lecture 25: Symmetric matrices and positive definiteness

Lecture 26: Complex matrices; fast fourier transform

Lecture 27: Positive definite matrices and minima

Lecture 28: Similar matrices and Jordan form

Lecture 29: Singular value decomposition

Lecture 30: Linear transformations and their matrices

Lecture 31: Change of basis; image compression

Lecture 32: Quiz 3 review

Lecture 33: Left and right inverses; pseudoinverse

Lecture 34: Final course review