Unit 1 · 0/7 Vectors
1.1 this Vectors in the Plane and in Space 1.2 opens Linear Combinations 1.3 Span 1.4 opens The Dot Product and Length 1.5 Angles and Orthogonality 1.6 Lines and Planes 1.7 The Cross Product Linear Algebra, Extended
Unit 2 · 0/6 Systems of Linear Equations
2.1 Two Pictures of a Linear System 2.2 Gaussian Elimination 2.3 Row Echelon and Reduced Row Echelon Form 2.4 Pivots, Free Variables and Solution Sets 2.5 Homogeneous Systems 2.6 Applications of Linear Systems
Unit 3 · 0/9 Matrix Algebra
3.1 The Matrix-Vector Product 3.2 Matrix Multiplication 3.3 The Algebra of Matrices 3.4 The Inverse of a Matrix 3.5 Computing an Inverse by Gauss-Jordan 3.6 Elementary Matrices 3.7 LU Factorization Linear Algebra, Extended 3.8 Transposes and Symmetric Matrices 3.9 The Invertible Matrix Theorem
Unit 4 · 0/5 Linear Transformations
4.1 Linear Transformations 4.2 The Matrix of a Linear Transformation 4.3 Rotations, Reflections, Shears and Projections 4.4 Composition Is Multiplication 4.5 One-to-One and Onto
Unit 5 · 0/5 Determinants
5.1 Determinants as Area and Volume 5.2 Cofactor Expansion 5.3 Row Operations and Determinants 5.4 The Product Rule and Invertibility 5.5 Cramer's Rule and the Adjugate Linear Algebra, Extended
Unit 6 · 0/8 Vector Spaces
6.1 Vector Spaces and Subspaces 6.2 Null Space and Column Space 6.3 Linear Independence 6.4 Basis 6.5 Dimension and Rank 6.6 The Rank-Nullity Theorem 6.7 The Four Fundamental Subspaces Linear Algebra, Extended 6.8 Coordinates and Change of Basis
Unit 7 · 0/6 Eigenvalues and Eigenvectors
7.1 Eigenvectors and Eigenvalues 7.2 The Characteristic Polynomial 7.3 Diagonalization 7.4 Powers of a Matrix and Markov Chains 7.5 Complex Eigenvalues and Rotation Linear Algebra, Extended 7.6 Systems of Differential Equations Linear Algebra, Extended
Unit 8 · 0/6 Orthogonality and Least Squares
8.1 Orthogonal Sets and Bases 8.2 Projections 8.3 The Gram-Schmidt Process 8.4 QR Factorization Linear Algebra, Extended 8.5 Least Squares 8.6 Orthogonal Matrices
Unit 9 · 0/5 Symmetric Matrices and the SVD
9.1 The Spectral Theorem 9.2 Quadratic Forms and Positive Definite Matrices 9.3 The Singular Value Decomposition Linear Algebra, Extended 9.4 Low-Rank Approximation and Compression Linear Algebra, Extended 9.5 The Pseudoinverse Linear Algebra, Extended