Linear Algebra and Its Applications, Global Edition

Cover
Title Page
Copyright
Dedication
About the Authors
Contents
Applications Index
Preface
Get the most out of MyLab Math
Resources for Success
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
	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 Rn
	2.9 Dimension and Rank
	Projects
	Supplementary Exercises
Chapter 3: Determinants
	Introductory Example: Weighing Diamonds
	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: Discrete-Time Signals and Digital Signal Processing
	4.1 Vector Spaces and Subspaces
	4.2 Null Spaces, Column Spaces, Row 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 Applications to 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 Linear Models
	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 Image Processing 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
	Project
	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
	Project
	Supplementary Exercises
Appendixes
	Appendix A: Uniqueness of the Reduced Echelon Form
	Appendix B: Complex Numbers
Credits
Glossary
Answers to Odd-Numbered Exercises
Index
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	B
	C
	D
	E
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	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
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	T
	U
	V
	W
	Z
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