18.06SC Linear Algebra

18.06SC Linear Algebra (Fall 2011, MIT OCW). Taught by Prof. Gilbert Strang, this course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include: a complete set of lecture videos, summary notes, problem solving videos, and a full set of exams and solutions. (from


Unit I. Ax=b and the Four Subspaces
Lecture 01 - The Geometry of Linear Equations
Lecture 02 - An Overview of Key Ideas
Lecture 03 - Elimination with Matrices
Lecture 04 - Multiplication and Inverse Matrices
Lecture 05 - Factorization into A = LU
Lecture 06 - Transposes, Permutations, Vector Spaces
Lecture 07 - Column Space and Nullspace
Lecture 08 - Solving Ax = 0: Pivot Variables, Special Solutions
Lecture 09 - Solving Ax = b: Row Reduced form R
Lecture 10 - Independence, Basis and Dimension
Lecture 11 - The Four Fundamental Subspaces
Lecture 12 - Matrix Spaces; Rank 1; Small World Graphs
Lecture 13 - Graphs, Networks, Incidence Matrices
Lecture 14 - Exam 1 Review
Unit II. Least Squares, Determinants and Eigenvalues
Lecture 15 - Orthogonal Vectors and Subspaces
Lecture 16 - Projections onto Subspaces
Lecture 17 - Projection Matrices and Least Squares
Lecture 18 - Orthogonal Matrices and Gram-Schmidt
Lecture 19 - Properties of Determinants
Lecture 20 - Determinant Formulas and Cofactors
Lecture 21 - Cramer's Rule, Inverse Matrix and Volume
Lecture 22 - Eigenvalues and Eigenvectors
Lecture 23 - Diagonalization and Powers of A
Lecture 24 - Differential Equations and exp(At)
Lecture 25 - Markov Matrices; Fourier series
Lecture 26 - Exam 2 Review
Unit III. Positive Definite Matrices and Applications
Lecture 27 - Symmetric Matrices and Positive Definiteness
Lecture 28 - Complex Matrices; Fast Fourier Transform
Lecture 29 - Positive Definite Matrices and Minima
Lecture 30 - Similar Matrices and Jordan Form
Lecture 31 - Singular Value Decomposition
Lecture 32 - Linear Transformations and their Matrices
Lecture 33 - Change of Basis; Image Compression
Lecture 34 - Left and Right Inverses; Pseudoinverse
Lecture 35 - Exam 3 Review
Lecture 36 - Final Course Review

18.06SC Linear Algebra
Instructors: Prof. Gilbert Strang. A complete set of lecture videos. Summary notes. Problem solving videos. Problem sets with solutions. A full set of exams and solutions.
18.085 Computational Science and Engineering I
Instructors: Prof. Gilbert Strang. Exams and Solutions. Subtitles/Transcript. Assignments and Solutions. Applied linear algebra, Applied differential equations, Fourier methods, and Algorithms.