Linear Algebra MIT 18.06 (OCW)
Lectures by G. Strang, 2005
List of Topics
- The Geometry of Linear Equations link
- Elimination with Matrices link
- Multiplication and Inverse Matrices link
- Factorization into $A = LU$ link
- Transposes, Permutations, Spaces $\mathbb R^n$ link
- Vector Subspaces: Column Space and Nullspace link
- Solving $A \mathbf x = \mathbf 0$: Pivot Variables, Special Solutions link
- Solving $A \mathbf x = \mathbf b$: Row Reduced Form $R$ link
- Independence, Basis, and Dimension link
- The Four Fundamental Subspaces link
- Matrix Spaces; Rank 1 Matrices; Small World Graphs link
- Graphs, Networks, Incidence Matrices link
- Quiz 1 Review link
- Orthogonality: Orthogonal Vectors and Orthogonal Subspaces link
- Projection onto Subspaces link
- Projection Matrices and Least Squares link
- Orthogonal Matrices and Gram-Schmidt link
- Properties of Determinants link
- Determinant Formulas and Cofactors link
- Cramer’s Rule, Inverse Matrix, and Volume link
- Eigenvalues and Eigenvectors link
- Matrix Diagonalization and Powers of $A$ link
- Differential Equations and $\exp(At)$ link
- Markov Matrices; Fourier Series link
- Quiz 2 Review link
- Symmetric Matrices and Positive Definiteness link
- Complex Matrices; Fast Fourier Transform link
- Positive-Definite Matrices and Minima link
- Similar Matrices and Jordan Form link
- Singular Value Decomposition link
- Linear Transformations and Their Matrices link
- Change of Basis; Image Compression link
- Quiz 3 Review link
- General Inverses: Left and Right Inverses; Pseudoinverse link
- Final Course Review link