Licence:
Course Description:
This is a basic course on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Lectures:
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 R^n
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
In this lecture, Professor Gilbert Strang provides an introduction to eigenvalues and eigenvectors.
Lecture 22 - Diagonalization and Powers of A
Lecture 23 - Differential Equations and exp(At)
Lecture 24 - Markov Matrices; Fourier Series
Lecture 25 - Quiz 2 Review
Lecture 26 - Symmetric Matrices and Positive Definiteness
Lecture 27 - Complex Matrices; Fast Fourier Transform
Lecture 28 - Positive Definite Matrices and Minima
Lecture 29 - Similar Matrices and Jordan Form
Lecture 30 - Singular Value Decomposition
Lecture 31 - Linear Transformations and Their Matrices
Lecture 32 - Change of Basis; Image Compression
Lecture 33 - Quiz 3 Review
Lecture 34 - Left and Right Inverses; Pseudoinverse
Lecture 35 - Final Course Review
Source: http://academicearth.org/courses/linear-algebra
