Linear Algebra and Its Applications - Global 6th Edition

Fosters the concepts and skills needed for future careers
Linear Algebra and Its Applications offers a modern elementary introduction with broad, relevant applications. With traditional texts, the early stages of the course are relatively easy as material is presented in a familiar, concrete setting, but students often hit a wall when abstract concepts are introduced. Certain concepts fundamental to the study of linear algebra (such as linear independence, vector space, and linear transformations) require time to assimilate GÇö and students' understanding of them is vital.
Lay, Lay, and McDonald make these concepts more accessible by introducing them early in a familiar, concrete setting, developing them gradually, and returning to them throughout the text so that students can grasp them when they are discussed in the abstract. The 6th Edition offers exciting new material, examples, and online resources, along with new topics, vignettes, and applications.

Reach every student by pairing this text with MyLab Math
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MyLab Math should only be purchased when required by an instructor. Please be sure you have the correct ISBN and Course ID. Instructors, contact your Pearson representative for more information.

This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.
This package includes MyLab.
For courses in Linear Algebra.

List of contents

About the Authors

Preface

A Note to Students

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 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

1. Uniqueness of the Reduced Echelon Form
2. Complex Numbers

Credits

Glossary

Answers to Odd-Numbered Exercises

Index

About the author

David C. Lay, University of Maryland–College Park
Steven R. Lay, Lee University
Judi J. McDonald, Washington State University

Summary

Learn key concepts of linear algebra to equip yourself in your studies and future career.

Linear Algebra and Its Applications 6^th edition by Steven R. Lay, Judi J. McDonald and David C. Lay is an excellent introductory guide to the principles and foundations of practical linear algebra.
With its learner-friendly approach, the textbook starts with easier material, building confidence by introducing typically challenging concepts early on and gradually developing them. The book revisits those concepts throughout, ensuring you do not become overwhelmed when abstract concepts are introduced, as you progress with your learning.
The latest edition provides new and revised content, with a range of features, including:

• A broad range of introductory vignettes, application examples, and online resources
• New material and topics to consolidate and enhance your understanding of the subject
• New, modernised applications to prepare your learning of the most innovative topics, such as machine learning, Artificial Intelligence, and digital signal processing

With an array of exercises and questions to support your learning, this textbook provides the tools you need to build on your understanding of linear algebra and succeed in your studies.
Also available with MyLab® Math
MyLab is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalises the learning experience and improves results for each student.
If you would like to purchase both the physical text and MyLab® Math, search for:
9781292351353 Linear Algebra and Its Applications, Global Edition, 6th edition plus MyLab Math with Pearson eText.
Package consists of:

• 9781292351216 Corporate Finance, Global Edition, 5th Edition
• 9781292351285 Corporate Finance, Global Edition, 5th Edition MyLab® Math with Pearson eText

MyLab® Math is not included. Students, if MyLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. MyLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.
This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content, which is especially relevant to students outside the United States.

Product details

• Authors: David Lay, David C. Lay, Lay Lay, Steven Lay, Steven R. Lay, Judi McDonald, Judi J. McDonald
• Publisher: Pearson Academic
• Languages: English
• Product format: Paperback / Softback
• Released: 31.07.2021
• EAN: 9781292351216
• ISBN: 978-1-292-35121-6
• Series: Pearson
• Subject: Natural sciences, medicine, IT, technology > Mathematics