18.06SC Linear Algebra (Fall 2011, MIT OCW) | Mathematics

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 ocw.mit.edu)

Introduction

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 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

References

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.