线性代数及其应用（第三版）（英文版）

.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 exercise

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 exercise

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 vector space
4.6 rank
4.7 change of basis
4.8 applications to difference equations
4.9 applications to markov chains
supplementary exercise

chapter 5 eigenvalues and eigenvectors

introductory example:dynamical systems
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 exercise

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 of inner product spaces
supplementary exercise

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 exercise

appendixes

a uniqueness of the reduced echelon form
b complex numbers

glossary
answers to odd-numbered exercises
index

.　　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
　　Important 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
　　Afew 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 exercises 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 Stud)' 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 the development and practice of linear algebra in science and engineering. Frequent Numerical Notes draw attention to issues in computing and distinguish between theoretical concepts, 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:
　　 wwv,.taylinalgebra.com or www. mymathiab.com
　　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 factofizations, 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.
　　SUPPLEMENTS
　　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 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 Corporation.
　　 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.
　　Finally, 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 C. 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 Stein, University of Connecticut
　　 James Thomas, Colorado State University
　　 Brian Turnquist, Bethel College
　　 Michael Ward, Western Oregon University
　　 Bruno Welfert, Arizona State 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; Weslie Lewis, marketing coordinator; and Marlene Thom and Jennifer Kerber, media producers. Saved for last are two special 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