Chapter 1 Linear Equations in LinearAlgebra
Introductory Example: Linear Models in Economics and Engineering
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax= b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in Business,Science, and Engineering
Projects
Supplementary Exercises
Chapter 2 Matrix Algebra
Introductory Example: Computer Models in Aircraft Design
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
2.6 The Leontief Input—Output Model
2.7 Applications to Computer Graphics
2.8 Subspaces of ?n
2.9 Dimension and Rank
Projects
Supplementary Exercises
Chapter 3 Determinants
Introductory Example: Random Paths and Distortion
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations
Projects
Supplementary Exercises
Chapter 4 Vector Spaces
Introductory Example: Space Flightand Control Systems
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces,and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Change of Basis
4.7 Digital Signal Processing
4.8 Applications to Difference Equations
Projects
Supplementary Exercises
Chapter 5 Eigenvalues and Eigenvectors
Introductory Example: Dynamical Systems and Spotted Owls
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvalues
5.6 Discrete Dynamical Systems
5.7 Applications to Differential Equations
5.8 Iterative Estimates for Eigenvalues
5.9 Markov Chains
Projects
Supplementary Exercises
Chapter 6 Orthogonality and Least Squares
Introductory Example: Artificial Intelligence and Machine Learning
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram—Schmidt Process
6.5 Least-Squares Problems
6.6 Machine Learning and LinearModels
6.7 Inner Product Spaces
6.8 Applications of Inner Product Spaces
Projects
Supplementary Exercises
Chapter 7 Symmetric Matrices and Quadratic Forms
Introductory Example: Multichannel Image Processing
7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
7.3 Constrained Optimization
7.4 The Singular Value Decomposition
7.5 Applications to ImageProcessing and Statistics
Projects
Supplementary Exercises
Chapter 8 The Geometry of Vector Spaces
Introductory Example: The Platonic Solids
8.1 Affine Combinations
8.2 Affine Independence
8.3 Convex Combinations
8.4 Hyperplanes
8.5 Polytopes
8.6 Curves and Surfaces
Projects
Supplementary Exercises
Chapter 9 Optimization
Introductory Example: The Berlin Airlift
9.1 Matrix Games
9.2 Linear Programming-Geometric Method
9.3 Linear Programming-Simplex Method
9.4 Duality
Projects
Supplementary Exercises
Chapter 10 Finite-State Markov Chains(Online Only)
Introductory Example: Googling Markov Chains
10.1 Introduction and Examples
10.2 The Steady-State Vector andGoogle's PageRank
10.3 Communication Classes
10.4 Classification of States andPeriodicity
10.5 The Fundamental Matrix
10.6 Markov Chains and BaseballStatistics
Appendixes
Uniqueness of the Reduced Echelon Form
Complex Numbers
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