Linear Algebra and Its Applications, Global Edition, 6th edition

Published by Pearson (July 14, 2021) © 2021
  • David C. Lay
  • Steven R. Lay
  • Judi J. McDonald

Title overview

Encourage your students to build their confidence in learning the basic principles of Linear Algebra.

Linear Algebra and Its Applications 6th edition supports your teaching as you provide the foundations your students need to understand practical linear algebra.

The edition's easy-to-follow layout covers the core concepts of linear algebra, gradually introducing more complex topics and returning to them throughout the book as a method to consolidate student understanding.

With a range of resources, this book is the ideal learning resource as you introduce your students to the primary concepts of linear algebra, from an elementary to a more advanced level.

Hallmark features of this title

Learner-Friendly Structure to Support Student Development
  • Starting with easier material and gradually developing complex concepts, the book ensures students do not hit a brick wall later in their learning.
  • The text continually returns to difficult topics, so students have more time to absorb and to review these critical concepts.
A Broad Range of Learning Aids to Improve Comprehension
  • Visualisation of Concepts throughout the chapters help students to grasp major points with the use of geometric interpretation.
  • Carefully selected Practice Problems before each exercise with complete set of solutions, focus on potential trouble spots in the exercise set or provide a “warm-up” for the exercises.

New and updated features of this title

Teach your subject with the most up-to-date course structure and content.
  • New topics and applications in this edition now prepare students with foundations for machine learning, artificial intelligence, data analysis, and digital signal processing.
  • A newly added Chapter 9, previously only available online, offers learning material on optimisation.
  • Reorganised chapters updated to reflect the importance of certain topics show how they relate to one another, such as moving Markov Chains in chapter 4 to the section on Eigenvalues and Eigenvectors in chapter 5.
Enhance your teaching and engage students by enabling them to apply learnt concepts.
  • End of chapter projects added to this edition encourage students to drill deeper into their exploration of various topics, encouraging them to use creativity in problem solving.
  • 'Reasonable Answers' sections are now included, offering advice and helping students analyse whether their answers are consistent with data in the given questions.

Key features

Features of Pearson eText for the 6th Edition

Linear Algebra and Its Applications 6th edition builds confidence as a comprehensive introduction to the key principles of linear algebra, equipping students with the needed knowledge and skills to progress in their academic journey.

With its learner-friendly approach, this textbook will assist your teaching by enhancing student engagement with the topics covered and ensure they do not become overwhelmed by complex concepts with chapters of gradually increasing difficulty.

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Table 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 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: 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 Gram—Schmidt 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 Programming–Geometric Method
  • 9.3 Linear Programming–Simplex 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

Author bios

David C. Lay, University of Maryland–College Park

Steven R. Lay, Lee University

Judi J. McDonald, Washington State University

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