Linear Algebra and Its Applications (Revised)

by Lay, David C.; Lay, Steven R.; McDonald, Judi J.

• ISBN13: 9780321982384
• ISBN10: 032198238X
• Edition: 5th
• Format: Hardcover
• Copyright: 2014-12-24
• Publisher: Pearson

About This Book

Linear Algebra and Its Applications, 5th Edition

Linear Algebra and Its Applications, 5th Edition, is a comprehensive textbook designed for undergraduate and graduate courses in linear algebra. This book is a go-to resource for students and educators alike, offering a detailed exploration of linear algebra principles and meeting scope and sequence requirements for typical introductory linear algebra courses.

Who Uses It?

Primarily, this book is used by students and instructors in introductory linear algebra courses at the college and university levels. It's also a valuable resource for anyone interested in understanding the basics of linear algebra, including professionals looking to refresh their knowledge or expand their understanding of mathematical principles.

History and Editions

The 5th edition of Linear Algebra and Its Applications has been updated to address user feedback, incorporating the latest research and discussions on linear algebra concepts. This edition includes detailed updates on clarity and accuracy, ensuring that students have a solid foundation in the material before moving on to more advanced topics. The book makes abstract concepts more accessible by introducing them early in a familiar, concrete setting and developing them gradually throughout the text.

Author and Other Works

David Lay, Steven Lay, and Judi McDonald are the authors of Linear Algebra and Its Applications. David Lay is known for his clear and concise writing style, which makes complex linear algebra concepts easier to understand. The authors have ensured that the text remains current and relevant by incorporating the latest research in the field.

Key Features

• Comprehensive Coverage: The book covers core concepts in linear algebra, including detailed explanations and examples.
• Gradual Development: The text introduces abstract concepts gradually, making them more accessible to students.
• Concrete Setting: The book starts with familiar, concrete settings (e.g., Rn) to help students understand complex concepts better.
• Instructor Resources: The book is complemented by instructor resources such as the Instructor’s Solutions Manual, which contains detailed solutions for all exercises, along with teaching notes for many sections.

Detailed Information

ISBNs and Formats

• Hardcover: ISBN-13: 9780321982384
• Publisher: Pearson
• Publication Date: March 16, 2025
• Number of Pages: 576 pages
• Language: English

Other Editions and Formats

• Related ISBNs:
• 9780134013473 (related ISBN for MyLab & Mastering products)
• 0134013476 (related ISBN for MyLab & Mastering products)

Rental Options:

• Rental 90 Days Ready to Ship: $26.87 + $3.95 shipping = $30.82 total
• Used Ships 2-3 Days: $46.01 + $3.99 shipping = $50.00 total
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Publication Details

• Publisher: Pearson
• Publication Date: March 16, 2025
• Item Weight: Not specified
• Dimensions: Not specified

Instructor Resources:

• Instructor’s Solutions Manual: Available electronically for download in the Instructor Resource Center (www.pearsonhighered.com/lay) and MyMathLab.
• PowerPoint Slides: Available for download (ISBN 0-321-98264-9).

This detailed information section provides a quick reference for all the available formats and sources for Linear Algebra and Its Applications, 5th Edition, making it easier to find and access the book in the preferred format.

Author Biography

David C. Lay holds a B.A. from Aurora University (Illinois), and an M.A. and Ph.D. from the University of California at Los Angeles. David Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern, Germany. He has published more than 30 research articles on functional analysis and linear algebra. As a founding member of the NSF-sponsored Linear Algebra Curriculum Study Group, David Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also a coauthor of several mathematics texts, including Introduction to Functional Analysis with Angus E. Taylor, Calculus and Its Applications, with L. J. Goldstein and D. I. Schneider, and Linear Algebra Gems–Assets for Undergraduate Mathematics, with D. Carlson, C. R. Johnson, and A. D. Porter. David Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar—Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America’s Awards for Distinguished College or University Teaching of Mathematics. He has been elected by the university students to membership in Alpha Lambda Delta National Scholastic Honor Society and Golden Key National Honor Society. In 1989, Aurora University conferred on him the Outstanding Alumnus award. David Lay is a member of the American Mathematical Society, the Canadian Mathematical Society, the International Linear Algebra Society, the Mathematical Association of America, Sigma Xi, and the Society for Industrial and Applied Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.

 

Steven R. Lay began his teaching career at Aurora University (Illinois) in 1971, after earning an M.A. and a Ph.D. in mathematics from the University of California at Los Angeles. His career in mathematics was interrupted for eight years while serving as a missionary in Japan. Upon his return to the States in 1998, he joined the mathematics faculty at Lee University (Tennessee) and has been there ever since. Since then he has supported his brother David in refining and expanding the scope of this popular linear algebra text, including writing most of Chapters 8 and 9. Steven is also the author of three college-level mathematics texts: Convex Sets and Their Applications, Analysis with an Introduction to Proof, and Principles of Algebra. In 1985, Steven received the Excellence in Teaching Award at Aurora University. He and David, and their father, Dr. L. Clark Lay, are all distinguished mathematicians, and in 1989 they jointly received the Outstanding Alumnus award from their alma mater, Aurora University. In 2006, Steven was honored to receive the Excellence in Scholarship Award at Lee University. He is a member of the American Mathematical Society, the Mathematics Association of America, and the Association of Christians in the Mathematical Sciences.

 

Judi J. McDonald joins the authorship team after working closely with David on the fourth edition. She holds a B.Sc. in Mathematics from the University of Alberta, and an M.A. and Ph.D. from the University of Wisconsin. She is currently a professor at Washington State University. She has been an educator and research mathematician since the early 90s. She has more than 35 publications in linear algebra research journals. Several undergraduate and graduate students have written projects or theses on linear algebra under Judi’s supervision. She has also worked with the mathematics outreach project Math Central http://mathcentral.uregina.ca/ and continues to be passionate about mathematics education and outreach. Judi has received three teaching awards: two Inspiring Teaching awards at the University of Regina, and the Thomas Lutz College of Arts and Sciences Teaching Award at Washington State University. She has been an active member of the International Linear Algebra Society and the Association for Women in Mathematics throughout her career and has also been a member of the Canadian Mathematical Society, the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics.

 

Table of Contents

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

 

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

Supplementary Exercises

 

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

 

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

 

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

 

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

 

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

 

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

 

9. Optimization (Online Only)

Introductory Example: The Berlin Airlift

9.1 Matrix Games

9.2 Linear Programming—Geometric Method

9.3 Linear Programming—Simplex Method

9.4 Duality

 

10. Finite-State Markov Chains (Online Only)

Introductory Example: Googling Markov Chains

10.1 Introduction and Examples

10.2 The Steady-State Vector and Google's PageRank

10.3 Finite-State Markov Chains

10.4 Classification of States and Periodicity

10.5 The Fundamental Matrix

10.6 Markov Chains and Baseball Statistics

 

Appendices

A. Uniqueness of the Reduced Echelon Form

B. Complex Numbers