编辑推荐
本书是对线性代数及其有趣应用的基本介绍。在前两版的基础上，第三版提供了更多的形象化概念、应用（如1.6节中的列昂捷夫经济学模型、化学方程组和业务流），以及增强的Web支持。
作者简介
David C. Lay：美国奥罗拉大学学士，加州大学洛杉矶分校硕士、博士，教育家。1976年起开始在马里兰大学从事数学教学与研究工作，阿姆斯特丹大学、自由大学、德国凯撒斯劳滕工业大学访问学者，在函数分析和线性代数领域发表文章30余篇。美国国家科学基金会资助的线性代数课程研究小组的创始人，参与编写了《函数分析、积分及其应用导论》和《线性代数精粹》等书。
目录
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
Supplementary Exercises
CHAPTER 2 Matrix Alqebra
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
CHAPTER 3 Determinants
INTRODUCTORY EXAMPLE： Determinants in Analytic Geometry
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule， Volume， and Linear Transformations
Supplementary Exercises
CHAPTER 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 Veaor Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains
Supplementary Exercises
CHAPTER 5 Eiqenvalues and Eiqenvectors
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
CHAPTER 6 Orthogonality and Least Squares
INTRODUCTORY EXAMPLE： Readjusting the North American Datum
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 oflnner Product Spaces
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
Supplementary Exercises
Appendixes
A Uniqueness of the Reduced Echelon Form
B Complex Numbers
Glossary
Answers to Odd—Numbered Exercises
Index
序言
Preface
The response of students and teachers to the first two editions of Linear Algebra and Its Application has been most gratifying. This Third Edition offers even more visualization of concepts, along with enhanced technology support on the web for both students and instructors. As before, the text provides a modern elementary introduction to linear algebra and a broad selection of interesting applications. The material is accessible or students with the maturity that should come from successful completion of two semesters of college-level mathematics, usually calculus.
The main goal of the text is to help students master the basic concepts and skills they will use later in their careers. The topics here follow the recommendations of the Linear Algebra Curriculum Study Group, which were based on a careful investigation of the real needs of the students and a consensus among professionals in many disciplines that use linear algebra. Hopefully, this course will be one of the most useful and interesting mathematics classes taken as an undergraduate.
Distinctive Features
Early Introduction of Key Concepts
Many fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rn, and then gradually examined from different point of views, Later generalizations of these concepts appear as natural extensions of familiar ideas, visualized through the geometric intuition developed in Chapter 1. A major achievement of the text, I believe, is that the level of difficulty is fairly even throughout the course.
A Modern View of Matrix Multiplication
Good notation is crucial, and the text reflects the way scientists and engineers actually use linear algebra in practice. The definitions and proofs focus on the columns of a matrix rather than on the matrix entries. A central theme is to view a matrix-vector product Ax as a linear combination of the columns of A. This modern approach simplifies many arguments, and it ties vector space ideas into the study of linear systems.
Linear Transformations
Linear transformations form a “thread” that is woven into the fabric of the text.Their use enhances the geometric flavor of the text. In Chapter l, for instance, linear transformations provide a dynamic and graphical view of matrix-vector multiplication.
Eigenvalues and Dynamical Systems
Eigenvalues appear fairly early in the text, in Chapters 5 and 7. Because this material is Spread over several weeks, students have more time than usual to absorb and review these critical concepts. Eigenvalues are motivated by and applied to discrete and continuous dynamical systems, which appear in Sections l.10, 4.8, 4.9, and in five sections of Chapter 5. Some courses reach Chapter 5 after about five weeks by covering Sections 2.8 and 2.9 instead of Chapter 4. These two optional sections present all the vector space concepts from Chapter 4 needed for Chapter 5.
Orthogonality and Least-Squares Problems
These topics receive a more comprehensive treatment than is commonly found in beginning texts. The Linear Algebra Curriculum Study Group has emphasized the need for a substantial unit on orthogonality and least-squares problems, because orthogonality plays such an important role in computer calculations and numerical linear algebra and because inconsistent linear systems arise so often in practical work.
PEDAGOGICAL FEATURES
Applications
A broad selection of applications illustrates the Power of linear algebra to explain fundamental principles and simplify calculations in engineering, computer science, mathematics, physics, biology, economics, and statistics. Some applications appear in separate sections； others are treated in examples and exercises. In addition, each chapter opens with an introductory vignette that sets the stage for some application of linear algebra and provides a motivation for developing the mathematics that follows. Later, the text returns to that application in a section near the end of the chapter.
A Strong Geometric Emphasis
Every major concept in the course is given a geometric interpretation, because many students learn better when they can visualize an idea. There are substantially more drawings here than usual, and some of the figures have never appeared before in a linear algebra text.
Examples
This text devotes a larger proportion of its expository material to examples than do most linear algebra texts. There are more examples than an instructor would ordinarily present in class. But because the examples are written carefully, with lots of detail, students can read them on their own.
Theorems and Proofs
1brnportant results are stated as theorems. Other useful facts are displayed in tinted boxes, for easy reference. Most of the theorems have formal proofs, written with the beginning student in mind.In a few cases, the essential calculations of a proof are exhibited in a carefully chosen example.Some routine verifications are saved for exercises, when they will benefit students.
Practice Problems
A few carefully selected Practice Problems appear just before each exercise set. Complete solutions follow the exercise set. These problems either focus on potential trouble spots in the exercise set or provide a “warm-up” to the exercises, and the solutions often contain helpful hints or warnings about the homework.
Exercises
The abundant supply of exercises ranges from routine computations to conceptual questions that require more thought. A good number of innovative questions pinpoint conceptual difficulties that I have found on student papers over the years. Each exercise set is carefully arranged, in the same general order as the text； homework assignments are readily available when only part of a section is discussed. A notable feature of the exercise is their numerical simplicity. Problems “unfold” quickly, so students spend little time on numerical calculations. The exercises concentrate on teaching understanding rather than mechanical calculations.
True/False Questions
To encourage students to read all of the text and to think critically, I have developed 300 simple true/false questions that appear in 33 sections of the text, just after the computational problems. They can be answered directly from the text, and they prepare students for the conceptual problems that follow. Students appreciate these questions-after they get used to the importance of reading the text carefully. Based on class testing and discussions with students, I decided not to put the answers in the text. (The Study Guide tells the students where to find the answers to the odd-numbered questions.) An additional 150 true/false questions (mostly at the ends of chapters) test understanding of the material. The text does provide simple T/F answers to most of these questions, but it omits the justifications for the answers (which usually require some thought).
Writing Exercises
An ability to write coherent mathematical statements in English is essential for all students of linear algebra, not just those who may go to graduate school in mathematics. The text includes many exercises for which a written justification is part of the answer. Conceptual exercises that require a short proof usually contain hints that help a student get started. For all odd-numbered writing exercises, either a solution is included at the back of the text or a hint is given and the solution is in the Study Guide, described below.
Computational Topics
The text stresses the impact of the computer on both development and practice of liner algebra in science and engineering. Frequent Numerical Notes draw attention to issues in computing and distinguish between theoretical, such as matrix inversion, and computer implementations, such as LU factorizations.
SUPPORT ON THE WEB
An icon appears in the text margin whenever expanded or new supplementary material can be accessed through the web sites. The inside cover of this text, which lists text references to applications of linear algebra, also shows the locations of many of the icons.
The site www.laylinalgebra.com has everything a student needs to begin the course: the first chapter of the text, including answers for odd exercises； data files for the exercises； review sheets and practice exams； and the first chapter of the Study Guide (see below). Having all of this material for the first day of class avoids the problems that arise when a bookstore runs out of the text or the Study Guide.
Practice Tests and Review Sheets
Multiple copies of tests, with solutions, cover all the main topics in the text. They come directly from courses I have taught in recent years. Each review sheet identifies the key definitions, theorems, and skills from a specified portion of the text.
Case Studies and Application Projects
Seven Case Studies expand topics introduced at the beginning of each chapter, adding real-world data and opportunities for further exploration. Students will find these readings interesting. Some faculty may assign the projects contained therein. More than twenty Application Projects either extend existing topics in the text or introduce new applications, such as cubic splines, traffic flow, airline flight routes, dominance matrices in sports competition, and error-correcting codes. Some new mathematical applications are integration techniques, polynomial root location, conic sections, quadric surfaces, and extrema for functions of two variables.Numerical linear algebra topics, such as condition numbers, matrix factorizations, and the QR method for finding eigenvalues, are also included. Woven into each discussion are exercises that often involve large data sets (and thus require technology for their solution.)
Data Files
Hundreds of files contain data for about 900 numerical exercises in the text, Case Studies, and Application Projects. The data is stored in a variety of formats-for MATLAB, Maple, Mathematica, and the TI-83+/86/89 and HP48G graphic calculators. Accessing matrices and vectors for a particular problem requires only a few keystrokes, which eliminates data entry errors and saves time on homework.
Study Guide
I wrote this paperback student supplement to be an integral part of the course. The Study Guide (ISBN 0-201-77013-X) complements the text in several ways: (1) It shows the students how to learn linear algebra with suggestions for studying and discussions of the logical structure of various theorems and proofs. (2) It supplies detailed solutions for every third odd-numbered problem (which includes most key exercises) and solutions to every odd-numbered writing exercise for which the text's answer is only a “Hint.” (3) It provides a "lab manual" for using technology in the course, with additional help for [M] exercises and descriptions of appropriate commands for MATLAB, Maple, Mathematica, and graphic calculators, when those commands are first needed.
Instructor’s Edition
For the convenience of instructors, this special edition includes brief answers to all exercises. A Note to the Instructor at the beginning of the text provides a commentary on the design and organization of the text, to help instructors plan their courses. It also describes other support available for instructors.
Instructor's Technology Manuals
Each manual provides detailed guidance for integrating a specific software package or graphic calculator throughout the course, written by faculty who have already used the technology with this text.
ACKNOWLEDGMENTS
I am indeed grateful to many groups of people who have helped me over the years with various aspects of this book.
I want to thank Israel Gohberg and Robert Ellis for over fifteen years of research collaboration in linear algebra, which has so greatly shaped my view of linear algebra.
It has been my privilege to work with David Carlson, Charles Johnson, and Duane Porter on the Linear Algebra Curriculum Study Group. Their ideas about teaching linear a algebra have influenced this text in several important ways.
For assistance with the chapter opening examples and subsequent discussions, I thank Professor Thomas Polaski, Winthrop University； Professor Wassily Leontief. Institute for Economic Analysis, New York University； Clopper Almon, UniversitY of Maryland； David P. Young, Phantom Works, The Boeing Company； Roland Lamberson, Humboldt State University； and Russell Hardie, Chris Peterson, and the Earth Satellite C. orporation.
I want to thank the technology experts who labored on the various supplements for the Third Edition, preparing the data, writing notes for the instructors, writing technology notes for the students in the Study Guide, and sharing their projects with us: Jeremy Case (MATLAB), Taylor University； Douglas B. Meade (Maple), University of South Carolina； Lyle Cochran (Mathematica), Whitworth College, Michael Miller (TI calculators), Western Baptist College； and Thomas Polaski (HP-48G), Winthrop University. I also thank the two best undergraduate students I've had in recent years-Barker French and Ariel Weinberger—who updated the Second Edition's MATLAB data, checked all my calculations in the exercise solutions, and wrote drafts of some additional solutions.
FineLlly, I am grateful to Jane Day, San Jose State University, and Luz DeAlba, Drake University, for allowing us to continue to use their outstanding projects, which they developed during their ten years of work on this text. Their support, encouragement, and friendship have meant a lot to me.
I sincerely thank the following reviewers for their careful analyses and constructive suggestions:
Third Edition Reviewers and Class Testers
David Austin, Grand Valley State University
G. Barbanson, University of Texas at Austin
Kenneth Brown, Cornell University
David Carlson, San Diego State University
Greg Conner, Brigham Young University
Casey T. Cremins, University of Maryland
Sylvie Desjardins, Okanagan University College
Daniel Flath, University of South Alabama
Yuval Flicker, Ohio State University
Scott Fulton, Clarkson University
Herman Gollwitzer, Drexel University
Jeremy Haefner, University of Colorado at Colorado Springs
William Hager, University of Florida
John Hagood, Northern Arizona University
Willy Hereman, Colorado School of Mines
Alexander Hulpke, Colorado State University
Doug Hundley, Whitman College
James F Hurley, University of Connecticut
Jurgen Hurrelbrink, Louisiana State University
Jerry G. Ianni, La Guardia Community College (CUNY)
Hank Kuiper, Arizona State University
Ashok Kumar, Valdosta State University
Earl Kymala, California State University Sacramento
Kathryn Lenz, University of Minnesota-Duluth
Jaques Lewin, Syracuse University
En-Bing Lin, University of Toledo
Andrei Maltsev, University of Maryland
Abraham Mantell, Nassau Community College
Madhu Nayakkankuppam, University of Maryland-Baltimore County
Lei Ni, Stanford University
Gleb Novitchkov, Penn State University
Ralph Oberste-Vorth, University of South Florida
Dev Sinha, Brown University
Wasin So, San Jose State University
Ron Solomon, Ohio State University
Eugene Spiegel, University of Connecticut
Alan Stem: University of Connecticut
James Thomas, Colorado Stage University
Brian Turnquist, Bethel College
Michael Ward, Western Oregon University
Bruno Welfert, Arizona Stage University
Jack Xin, University of Texas at Austin
I am deeply grateful for the assistance of Thomas Polaski, of Winthrop University. He wrote the case studies and projects for the web, helped with exercise answers and solutions, handled the technology for the HP-48G, and was always available for advice about various decisions that had to be made. I also appreciate the mathematical assistance provided by Thomas Wegleitner, Deanna Richmond, and Paul Lorczak, who checked the accuracy of calculations in the text, and by Georgia K. Mederer, who proofread the page proofs for mathematical errors. Another person who helped to polish the final manuscript was Jane Hoover, of Lifland et al., Bookmakers. She supervised the copyediting and various stages of proofreading and coordinated with the typesetter. I greatly appreciate her help.
Finally, I sincerely thank the staff at Addison-Wesley for all their help with the development and production of the Third Edition. Rachel S. Reeve, project manager, was the key person for this edition, managing the more than fifty, people who worked on various parts of the project, frequently adjusting schedules, and calmly helping me find a way to get my part done. Other important members of the AW team were: Stefanie Borge, assistant editor； Beth Anderson, photo researcher； Karen Wernholm, production supervisor； Michael Boezi, marketing manager； Wescial friends who have guided the development of the book nearly from the beginning, giving wise counsel and encouragement and solving every problem that arose along the way-Greg Tobin, publisher, and Laurie Rosatone, sponsoring editor. Thank you both so much.
David C. Lay
文摘
版权页：
插图：
本书是对线性代数及其有趣应用的基本介绍。在前两版的基础上，第三版提供了更多的形象化概念、应用（如1.6节中的列昂捷夫经济学模型、化学方程组和业务流），以及增强的Web支持。
作者简介
David C. Lay：美国奥罗拉大学学士，加州大学洛杉矶分校硕士、博士，教育家。1976年起开始在马里兰大学从事数学教学与研究工作，阿姆斯特丹大学、自由大学、德国凯撒斯劳滕工业大学访问学者，在函数分析和线性代数领域发表文章30余篇。美国国家科学基金会资助的线性代数课程研究小组的创始人，参与编写了《函数分析、积分及其应用导论》和《线性代数精粹》等书。
目录
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
Supplementary Exercises
CHAPTER 2 Matrix Alqebra
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
CHAPTER 3 Determinants
INTRODUCTORY EXAMPLE： Determinants in Analytic Geometry
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule， Volume， and Linear Transformations
Supplementary Exercises
CHAPTER 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 Veaor Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains
Supplementary Exercises
CHAPTER 5 Eiqenvalues and Eiqenvectors
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
CHAPTER 6 Orthogonality and Least Squares
INTRODUCTORY EXAMPLE： Readjusting the North American Datum
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 oflnner Product Spaces
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
Supplementary Exercises
Appendixes
A Uniqueness of the Reduced Echelon Form
B Complex Numbers
Glossary
Answers to Odd—Numbered Exercises
Index
序言
Preface
The response of students and teachers to the first two editions of Linear Algebra and Its Application has been most gratifying. This Third Edition offers even more visualization of concepts, along with enhanced technology support on the web for both students and instructors. As before, the text provides a modern elementary introduction to linear algebra and a broad selection of interesting applications. The material is accessible or students with the maturity that should come from successful completion of two semesters of college-level mathematics, usually calculus.
The main goal of the text is to help students master the basic concepts and skills they will use later in their careers. The topics here follow the recommendations of the Linear Algebra Curriculum Study Group, which were based on a careful investigation of the real needs of the students and a consensus among professionals in many disciplines that use linear algebra. Hopefully, this course will be one of the most useful and interesting mathematics classes taken as an undergraduate.
Distinctive Features
Early Introduction of Key Concepts
Many fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rn, and then gradually examined from different point of views, Later generalizations of these concepts appear as natural extensions of familiar ideas, visualized through the geometric intuition developed in Chapter 1. A major achievement of the text, I believe, is that the level of difficulty is fairly even throughout the course.
A Modern View of Matrix Multiplication
Good notation is crucial, and the text reflects the way scientists and engineers actually use linear algebra in practice. The definitions and proofs focus on the columns of a matrix rather than on the matrix entries. A central theme is to view a matrix-vector product Ax as a linear combination of the columns of A. This modern approach simplifies many arguments, and it ties vector space ideas into the study of linear systems.
Linear Transformations
Linear transformations form a “thread” that is woven into the fabric of the text.Their use enhances the geometric flavor of the text. In Chapter l, for instance, linear transformations provide a dynamic and graphical view of matrix-vector multiplication.
Eigenvalues and Dynamical Systems
Eigenvalues appear fairly early in the text, in Chapters 5 and 7. Because this material is Spread over several weeks, students have more time than usual to absorb and review these critical concepts. Eigenvalues are motivated by and applied to discrete and continuous dynamical systems, which appear in Sections l.10, 4.8, 4.9, and in five sections of Chapter 5. Some courses reach Chapter 5 after about five weeks by covering Sections 2.8 and 2.9 instead of Chapter 4. These two optional sections present all the vector space concepts from Chapter 4 needed for Chapter 5.
Orthogonality and Least-Squares Problems
These topics receive a more comprehensive treatment than is commonly found in beginning texts. The Linear Algebra Curriculum Study Group has emphasized the need for a substantial unit on orthogonality and least-squares problems, because orthogonality plays such an important role in computer calculations and numerical linear algebra and because inconsistent linear systems arise so often in practical work.
PEDAGOGICAL FEATURES
Applications
A broad selection of applications illustrates the Power of linear algebra to explain fundamental principles and simplify calculations in engineering, computer science, mathematics, physics, biology, economics, and statistics. Some applications appear in separate sections； others are treated in examples and exercises. In addition, each chapter opens with an introductory vignette that sets the stage for some application of linear algebra and provides a motivation for developing the mathematics that follows. Later, the text returns to that application in a section near the end of the chapter.
A Strong Geometric Emphasis
Every major concept in the course is given a geometric interpretation, because many students learn better when they can visualize an idea. There are substantially more drawings here than usual, and some of the figures have never appeared before in a linear algebra text.
Examples
This text devotes a larger proportion of its expository material to examples than do most linear algebra texts. There are more examples than an instructor would ordinarily present in class. But because the examples are written carefully, with lots of detail, students can read them on their own.
Theorems and Proofs
1brnportant results are stated as theorems. Other useful facts are displayed in tinted boxes, for easy reference. Most of the theorems have formal proofs, written with the beginning student in mind.In a few cases, the essential calculations of a proof are exhibited in a carefully chosen example.Some routine verifications are saved for exercises, when they will benefit students.
Practice Problems
A few carefully selected Practice Problems appear just before each exercise set. Complete solutions follow the exercise set. These problems either focus on potential trouble spots in the exercise set or provide a “warm-up” to the exercises, and the solutions often contain helpful hints or warnings about the homework.
Exercises
The abundant supply of exercises ranges from routine computations to conceptual questions that require more thought. A good number of innovative questions pinpoint conceptual difficulties that I have found on student papers over the years. Each exercise set is carefully arranged, in the same general order as the text； homework assignments are readily available when only part of a section is discussed. A notable feature of the exercise is their numerical simplicity. Problems “unfold” quickly, so students spend little time on numerical calculations. The exercises concentrate on teaching understanding rather than mechanical calculations.
True/False Questions
To encourage students to read all of the text and to think critically, I have developed 300 simple true/false questions that appear in 33 sections of the text, just after the computational problems. They can be answered directly from the text, and they prepare students for the conceptual problems that follow. Students appreciate these questions-after they get used to the importance of reading the text carefully. Based on class testing and discussions with students, I decided not to put the answers in the text. (The Study Guide tells the students where to find the answers to the odd-numbered questions.) An additional 150 true/false questions (mostly at the ends of chapters) test understanding of the material. The text does provide simple T/F answers to most of these questions, but it omits the justifications for the answers (which usually require some thought).
Writing Exercises
An ability to write coherent mathematical statements in English is essential for all students of linear algebra, not just those who may go to graduate school in mathematics. The text includes many exercises for which a written justification is part of the answer. Conceptual exercises that require a short proof usually contain hints that help a student get started. For all odd-numbered writing exercises, either a solution is included at the back of the text or a hint is given and the solution is in the Study Guide, described below.
Computational Topics
The text stresses the impact of the computer on both development and practice of liner algebra in science and engineering. Frequent Numerical Notes draw attention to issues in computing and distinguish between theoretical, such as matrix inversion, and computer implementations, such as LU factorizations.
SUPPORT ON THE WEB
An icon appears in the text margin whenever expanded or new supplementary material can be accessed through the web sites. The inside cover of this text, which lists text references to applications of linear algebra, also shows the locations of many of the icons.
The site www.laylinalgebra.com has everything a student needs to begin the course: the first chapter of the text, including answers for odd exercises； data files for the exercises； review sheets and practice exams； and the first chapter of the Study Guide (see below). Having all of this material for the first day of class avoids the problems that arise when a bookstore runs out of the text or the Study Guide.
Practice Tests and Review Sheets
Multiple copies of tests, with solutions, cover all the main topics in the text. They come directly from courses I have taught in recent years. Each review sheet identifies the key definitions, theorems, and skills from a specified portion of the text.
Case Studies and Application Projects
Seven Case Studies expand topics introduced at the beginning of each chapter, adding real-world data and opportunities for further exploration. Students will find these readings interesting. Some faculty may assign the projects contained therein. More than twenty Application Projects either extend existing topics in the text or introduce new applications, such as cubic splines, traffic flow, airline flight routes, dominance matrices in sports competition, and error-correcting codes. Some new mathematical applications are integration techniques, polynomial root location, conic sections, quadric surfaces, and extrema for functions of two variables.Numerical linear algebra topics, such as condition numbers, matrix factorizations, and the QR method for finding eigenvalues, are also included. Woven into each discussion are exercises that often involve large data sets (and thus require technology for their solution.)
Data Files
Hundreds of files contain data for about 900 numerical exercises in the text, Case Studies, and Application Projects. The data is stored in a variety of formats-for MATLAB, Maple, Mathematica, and the TI-83+/86/89 and HP48G graphic calculators. Accessing matrices and vectors for a particular problem requires only a few keystrokes, which eliminates data entry errors and saves time on homework.
Study Guide
I wrote this paperback student supplement to be an integral part of the course. The Study Guide (ISBN 0-201-77013-X) complements the text in several ways: (1) It shows the students how to learn linear algebra with suggestions for studying and discussions of the logical structure of various theorems and proofs. (2) It supplies detailed solutions for every third odd-numbered problem (which includes most key exercises) and solutions to every odd-numbered writing exercise for which the text's answer is only a “Hint.” (3) It provides a "lab manual" for using technology in the course, with additional help for [M] exercises and descriptions of appropriate commands for MATLAB, Maple, Mathematica, and graphic calculators, when those commands are first needed.
Instructor’s Edition
For the convenience of instructors, this special edition includes brief answers to all exercises. A Note to the Instructor at the beginning of the text provides a commentary on the design and organization of the text, to help instructors plan their courses. It also describes other support available for instructors.
Instructor's Technology Manuals
Each manual provides detailed guidance for integrating a specific software package or graphic calculator throughout the course, written by faculty who have already used the technology with this text.
ACKNOWLEDGMENTS
I am indeed grateful to many groups of people who have helped me over the years with various aspects of this book.
I want to thank Israel Gohberg and Robert Ellis for over fifteen years of research collaboration in linear algebra, which has so greatly shaped my view of linear algebra.
It has been my privilege to work with David Carlson, Charles Johnson, and Duane Porter on the Linear Algebra Curriculum Study Group. Their ideas about teaching linear a algebra have influenced this text in several important ways.
For assistance with the chapter opening examples and subsequent discussions, I thank Professor Thomas Polaski, Winthrop University； Professor Wassily Leontief. Institute for Economic Analysis, New York University； Clopper Almon, UniversitY of Maryland； David P. Young, Phantom Works, The Boeing Company； Roland Lamberson, Humboldt State University； and Russell Hardie, Chris Peterson, and the Earth Satellite C. orporation.
I want to thank the technology experts who labored on the various supplements for the Third Edition, preparing the data, writing notes for the instructors, writing technology notes for the students in the Study Guide, and sharing their projects with us: Jeremy Case (MATLAB), Taylor University； Douglas B. Meade (Maple), University of South Carolina； Lyle Cochran (Mathematica), Whitworth College, Michael Miller (TI calculators), Western Baptist College； and Thomas Polaski (HP-48G), Winthrop University. I also thank the two best undergraduate students I've had in recent years-Barker French and Ariel Weinberger—who updated the Second Edition's MATLAB data, checked all my calculations in the exercise solutions, and wrote drafts of some additional solutions.
FineLlly, I am grateful to Jane Day, San Jose State University, and Luz DeAlba, Drake University, for allowing us to continue to use their outstanding projects, which they developed during their ten years of work on this text. Their support, encouragement, and friendship have meant a lot to me.
I sincerely thank the following reviewers for their careful analyses and constructive suggestions:
Third Edition Reviewers and Class Testers
David Austin, Grand Valley State University
G. Barbanson, University of Texas at Austin
Kenneth Brown, Cornell University
David Carlson, San Diego State University
Greg Conner, Brigham Young University
Casey T. Cremins, University of Maryland
Sylvie Desjardins, Okanagan University College
Daniel Flath, University of South Alabama
Yuval Flicker, Ohio State University
Scott Fulton, Clarkson University
Herman Gollwitzer, Drexel University
Jeremy Haefner, University of Colorado at Colorado Springs
William Hager, University of Florida
John Hagood, Northern Arizona University
Willy Hereman, Colorado School of Mines
Alexander Hulpke, Colorado State University
Doug Hundley, Whitman College
James F Hurley, University of Connecticut
Jurgen Hurrelbrink, Louisiana State University
Jerry G. Ianni, La Guardia Community College (CUNY)
Hank Kuiper, Arizona State University
Ashok Kumar, Valdosta State University
Earl Kymala, California State University Sacramento
Kathryn Lenz, University of Minnesota-Duluth
Jaques Lewin, Syracuse University
En-Bing Lin, University of Toledo
Andrei Maltsev, University of Maryland
Abraham Mantell, Nassau Community College
Madhu Nayakkankuppam, University of Maryland-Baltimore County
Lei Ni, Stanford University
Gleb Novitchkov, Penn State University
Ralph Oberste-Vorth, University of South Florida
Dev Sinha, Brown University
Wasin So, San Jose State University
Ron Solomon, Ohio State University
Eugene Spiegel, University of Connecticut
Alan Stem: University of Connecticut
James Thomas, Colorado Stage University
Brian Turnquist, Bethel College
Michael Ward, Western Oregon University
Bruno Welfert, Arizona Stage University
Jack Xin, University of Texas at Austin
I am deeply grateful for the assistance of Thomas Polaski, of Winthrop University. He wrote the case studies and projects for the web, helped with exercise answers and solutions, handled the technology for the HP-48G, and was always available for advice about various decisions that had to be made. I also appreciate the mathematical assistance provided by Thomas Wegleitner, Deanna Richmond, and Paul Lorczak, who checked the accuracy of calculations in the text, and by Georgia K. Mederer, who proofread the page proofs for mathematical errors. Another person who helped to polish the final manuscript was Jane Hoover, of Lifland et al., Bookmakers. She supervised the copyediting and various stages of proofreading and coordinated with the typesetter. I greatly appreciate her help.
Finally, I sincerely thank the staff at Addison-Wesley for all their help with the development and production of the Third Edition. Rachel S. Reeve, project manager, was the key person for this edition, managing the more than fifty, people who worked on various parts of the project, frequently adjusting schedules, and calmly helping me find a way to get my part done. Other important members of the AW team were: Stefanie Borge, assistant editor； Beth Anderson, photo researcher； Karen Wernholm, production supervisor； Michael Boezi, marketing manager； Wescial friends who have guided the development of the book nearly from the beginning, giving wise counsel and encouragement and solving every problem that arose along the way-Greg Tobin, publisher, and Laurie Rosatone, sponsoring editor. Thank you both so much.
David C. Lay
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| ISBN | 9787121285912 |
|---|---|
| 出版社 | 电子工业出版社 |
| 作者 | 戴维 C.莱 (David C.Lay) |
| 尺寸 | 16 |