Introduction to Vectors / 1: |
Vectors and Linear Combinations / 1.1: |
Lengths and Dot Products / 1.2: |
Matrices / 1.3: |
Solving Linear Equations / 2: |
Vectors and Linear Equations / 2.1: |
The Idea of Elimination / 2.2: |
Elimination Using Matrices / 2.3: |
Rules for Matrix Operations / 2.4: |
Inverse Matrices / 2.5: |
Elimination = Factorization: A = LU / 2.6: |
Transposes and Permutations / 2.7: |
Vector Spaces and Subspaces / 3: |
Spaces of Vectors / 3.1: |
The Nullspace of A: Solving Ax = 0 and Rx = 0 / 3.2: |
The Complete Solution to Ax = b / 3.3: |
Independence, Basis and Dimension / 3.4: |
Dimensions of the Four Subspaces / 3.5: |
Orthogonality / 4: |
Orthogonality of the Four Subspaces / 4.1: |
Projections / 4.2: |
Least Squares Approximations / 4.3: |
Orthonormal Bases and Gram-Schmidt / 4.4: |
Determinants / 5: |
The Properties of Determinants / 5.1: |
Permutations and Cofactors / 5.2: |
Cramer's Rule, Inverses, and Volumes / 5.3: |
Eigenvalues and Eigenvectors / 6: |
Introduction to Eigenvalues / 6.1: |
Diagonalizing a Matrix / 6.2: |
Systems of Differential Equations / 6.3: |
Symmetric Matrices / 6.4: |
Positive Definite Matrices / 6.5: |
The Singular Value Decomposition (SVD) / 7: |
Image Processing by Linear Algebra / 7.1: |
Bases and Matrices in the SVD / 7.2: |
Principal Component Analysis (PCA by the SVD) / 7.3: |
The Geometry of the SVD / 7.4: |
Linear Transformations / 8: |
The Idea of a Linear Transformation / 8.1: |
The Matrix of a Linear Transformation / 8.2: |
The Search for a Good Basis / 8.3: |
Complex Vectors and Matrices / 9: |
Complex Numbers / 9.1: |
Hermitian and Unitary Matrices / 9.2: |
The Fast Fourier Transform / 9.3: |
Applications / 10: |
Graphs and Networks / 10.1: |
Matrices in Engineering / 10.2: |
Markov Matrices, Population, and Economics / 10.3: |
Linear Programming / 10.4: |
Fourier Series: Linear Algebra for Functions / 10.5: |
Computer Graphics / 10.6: |
Linear Algebra for Cryptography / 10.7: |
Numerical Linear Algebra / 11: |
Gaussian Elimination in Practice / 11.1: |
Norms and Condition Numbers / 11.2: |
Iterative Methods and Preconditioned / 11.3: |
Linear Algebra in Probability & Statistics / 12: |
Mean, Variance, and Probability / 12.1: |
Covariance Matrices and Joint Probabilities / 12.2: |
Multivariate Gaussian and Weighted Least Squares / 12.3: |
Matrix Factorizations |
Index |
Sex Great Theorems/Linear Algebra in a Nutshell |
Introduction to Vectors / 1: |
Vectors and Linear Combinations / 1.1: |
Lengths and Dot Products / 1.2: |
Matrices / 1.3: |
Solving Linear Equations / 2: |
Vectors and Linear Equations / 2.1: |