Linear Algebra and Its Applications, Globa...

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About the Authors Preface A Note to StudentsChapter 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 InputOutput 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 GramSchmidt 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 ProgrammingGeometric Method
9.3 Linear ProgrammingSimplex 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 Credits Glossary Answers to Odd-Numbered Exercises Index