For courses in Linear Algebra.
Fosters the concepts and skillsneeded for future careers
Linear Algebra and ItsApplications offers a modern elementary introduction with broad, relevantapplications. With traditional texts, the early stages of the course arerelatively easy as material is presented in a familiar, concrete setting, butstudents often hit a wall when abstract concepts are introduced. Certainconcepts fundamental to the study of linear algebra (such as linearindependence, vector space, and linear transformations) require time toassimilate ― and students' understanding of them is vital.
Lay, Lay, and McDonald make theseconcepts more accessible by introducing them early in a familiar, concrete ℝn setting, developing them gradually, and returning to themthroughout the text so that students can grasp them when they are discussed inthe abstract. The 6th Edition offers exciting new material, examples,and online resources, along with new topics, vignettes, and applications.
Author(s): David Lay, Steven Lay, Judi McDonald
Edition: 6 (Global Edition)
Publisher: Pearson
Year: 2021
Language: English
Pages: 670
Tags: linear, algebra
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
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
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