Book:Gilbert Strang/Introduction to Linear Algebra/Fifth Edition

Subject Matter

 * Linear Algebra

Contents

 * 1 Introduction to Vectors
 * 1.1 Vectors and Linear Combinations
 * 1.2 Lengths and Dot Products
 * 1.3 Matrices


 * 2 Solving Linear Equations
 * 2.1 Vectors and Linear Equations
 * 2.2 The Idea of Elimination
 * 2.3 Elimination Using Matrices
 * 2.4 Rules for Matrix Operations
 * 2.5 Inverse Matrices
 * 2.6 Elimination = Factorization: $A = L U$
 * 2.7 Transposes and Permutations


 * 3 Vector Spaces and Subspaces
 * 3.1 Spaces of Vectors
 * 3.2 The Nullspace of A: Solving $A x = 0$ and $R x = 0$
 * 3.3 The Complete Solution to $A x = b$
 * 3.4 Independence, Basis and Dimension
 * 3.5 Dimensions of the Four Subspaces


 * 4 Orthogonality
 * 4.1 Orthogonality of the Four Subspaces
 * 4.2 Projections
 * 4.3 Least Squares Approximations
 * 4.4 Orthonormal Bases and Gram-Schmidt


 * 5 Determinants
 * 5.1 The Properties of Determinants
 * 5.2 Permutations and Cofactors
 * 5.3 Cramer’s Rule, Inverses, and Volumes


 * 6 Eigenvalues and Eigenvectors
 * 6.1 Introduction to Eigenvalues
 * 6.2 Diagonalizing a Matrix
 * 6.3 Systems of Differential Equations
 * 6.4 Symmetric Matrices
 * 6.5 Positive Definite Matrices


 * 7 The Singular Value Decomposition (SVD)
 * 7.1 Image Processing by Linear Algebra
 * 7.2 Bases and Matrices in the SVD
 * 7.3 Principal Component Analysis (PCA by the SVD)
 * 7.4 The Geometry of the SVD


 * 8 Linear Transformations
 * 8.1 The Idea of a Linear Transformation
 * 8.2 The Matrix of a Linear Transformation
 * 8.3 The Search for a Good Basis


 * 9 Complex Vectors and Matrices
 * 9.1 Complex Numbers
 * 9.2 Hermitian and Unitary Matrices
 * 9.3 The Fast Fourier Transform


 * 10 Applications
 * 10.1 Graphs and Networks
 * 10.2 Matrices in Engineering
 * 10.3 Markov Matrices, Population, and Economics
 * 10.4 Linear Programming
 * 10.5 Fourier Series: Linear Algebra for Functions
 * 10.6 Computer Graphics
 * 10.7 Linear Algebra for Cryptography


 * 11 Numerical Linear Algebra
 * 11.1 Gaussian Elimination in Practice
 * 11.2 Norms and Condition Numbers
 * 11.3 Iterative Methods and Preconditioners


 * 12 Linear Algebra in Probability & Statistics
 * 12.1 Mean, Variance, and Probability
 * 12.2 Covariance Matrices and Joint Probabilities
 * 12.3 Multivariate Gaussian andWeighted Least Squares


 * Matrix Factorizations
 * Index
 * Six Great Theorems / Linear Algebra in a Nutshell