Linear Algebra and Its Applications, 4th Edition

Cover
Title Page
Copyright Page
About the Author
Contents
Preface
ACKNOWLEDGMENTS
A Note to Students
Chapter 1 Linear Equations in Linear Algebra
	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
	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 R[sup(n)]
	2.9 Dimension and Rank
	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
	Supplementary Exercises
Chapter 4 Vector Spaces
	INTRODUCTORY EXAMPLE: Space Flight and 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 Rank
	4.7 Change of Basis
	4.8 Applications to Difference Equations
	4.9 Applications to Markov Chains
	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
	Supplementary Exercises
Chapter 6 Orthogonality and Least Squares
	INTRODUCTORY EXAMPLE: The North American Datum and GPS Navigation
	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 Applications to Linear Models
	6.7 Inner Product Spaces
	6.8 Applications of Inner Product Spaces
	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 Image Processing and Statistics
	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
Appendixes
	A: Uniqueness of the Reduced Echelon Form
	B: Complex Numbers
Glossary
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Answers to Odd-Numbered Exercises
Index
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Photo Credits