线性代数(英文影印版.第7版)

3 Linear Independence
4 Basis and Dimension
5 Change of Basis
6 Row Space and Column Space
MATLAB Exercises
Chapter Test A
Chapter Test B
4 LINEAR TRANSFORMATIONS
1 Definition and Examples
2 Matrix Representations of Linear Transformations
3 Similarity
MATLAB Exercises
Chapter Test A
Chapter Test B
5 ORTHOGONALITY
1 The Scalar Product in Rn
2 Orthogonal Subspaces
3 Least Squares Problems
4 Inner Product Spaces..
5 Orthonormal Sets
6 The Gram-Schmidt Orthogonalization Process
7 Orthogonal Polynomials
MATLAB Exercises
Chapter Test A
Chapter Test B
6 EIGENVALUES
1 Eigenvalues and Eigenvectors
2 Systems of Linear Differential Equations
3 Diagonalization
4 Hermitian Matrices
5 The Singular Value Decomposition
G Quadratic Forms
7 Positive Definite Matrices
8 Nonnegative Matrices
MATLAB Exercises
Chapter Test A
Chapter Test B
7 NUMERICAL LINEAR ALGEBRA
1 Floating-Point Numbers
2 Gaussian Elimination
3 Pivoting Strategies
4 Matrix Norms and Condition Numbers
5 Orthogonal Transformations
6 The Eigenvalue Problem
7 Least Squares Problems
MATLAB Exercises
Chapter Test A
Chapter Test B
8 ITERATIVE METHODS
9 CANONICAL FORMS
APPENDIX: MATLAB
BIBLIOGRAPHY
ANSWERS TO SELECTED EXERCISES
INDEX...

.　　The URL for the site is listed in the Supplementary Materials section of this Preface.
　　6. The ATLAST Companion Computer Manual, Second edition
　　ATLAST (Augmenting the Teaching of Linear Algebra using Software Tools) is an NSF sponsored project to encourage and facilitate the use of software in the teaching of linear algebra. During a five year period, 1992-1997, the ATLAST Project conducted 18 faculty workshops using the MATLAB software package. Participants in these workshops designed computer exercises, projects, and lesson plans for software-based teaching of linear algebra. A selection of these materials was published as a manual in 1997. That manual has now been greatly expanded in a new edition, ATLAST Computer Exercises for Linear Algebra, Second edition (Prentice Hall, 2003). The ATLAST book is available as a free companion volume to this textbook when the two books are wrapped together for class orders. The ISBN for ordering the two-book bundle is given in the Supplementary Materials section of this Preface. The collection of software tools (M-files) developed to accompany the ATLAST book may be downloaded from the ATLAST Web site. Mathematica users can download the collection of ATLASTMathematica Notebooks that has been developed by Richard Neidinger. ..
　　7. Companion Manuals
　　A number of other MATLAB and Maple computer manuals are available from Prentice-Hall. These are offered at no extra cost when ordered with the textbook as a two-book bundle. The list of bundles and the corresponding ISBN's for placing orders are given in the Supplementary Materials section of this Preface.
　　8. Student Guide to Linear Algebra with Applications
　　A new student study guide has been developed to accompany this edition. The guide is described in the Supplementary Materials section of this preface.
　　9. Other Changes
　　In preparing the seventh edition, the author has carefully reviewed every section of the book. In addition to the major changes that have been listed, many minor improvements have been made throughout the text.
　　COMPUTER EXERCISES
　　This edition contains a section of computing exercises at the end of each chapter. These exercises are based on the software package MATLAB. The MATLAB Appendix in the book explains the basics of using the software. MATLAB has the advantage that it is a powerful tool for matrix computations and yet it is easy to learn. After reading the Appendix, students should be able to do the computing exercises without having to refer to any other software books or manuals. To help students get started we recommend one 50 minute classroom demonstration of the software. The assignments can be done either as ordinary homework assignments or as part of a formally scheduled computer laboratory course.
　　As mentioned previously, the ATLAST book is available as a companion volume to supplement the computer exercises in this book. Each of the eight chapters of the ATLAST book contains a section of short exercises and a section of longer projects.
　　While the course can be taught without any reference to the computer, we believe that computer exercises can greatly enhance student learning and provide a new dimension to linear algebra education. The Linear Algebra Curriculum Study Group has recommended that technology be used for a first course in linear algebra. and this view is generally accepted throughout the greater mathematics community.
　　OVERVIEW OF TEXT
　　This book is suitable for either a sophomore-level course or for a junior/senior-level course. The student should have some familiarity with the basics of differential and integral calculus. This prerequisite can be met by either one semester or two quarters of elementary calculus.
　　If the text is used for a sophomore-level course, the instructor should probably spend more time on the early chapters and Omit many of the sections in the later chapters. For more advanced courses a quick review of many of the topics in the first two chapters and then a more complete coverage of the later chapters would be appropriate. The explanations in the text are given in sufficient detail so that beginning students should have little trouble reading and understanding the material. To further aid the student, a large number of examples have been worked out completely. Additionally, computer exercises at the end of each chapter give students the opportunity to perform numerical experiments and try to generalize the results. Applications are presented throughout the book. These applications can be used to motivate new material or to illustrate the relevance of material that has already been covered.
　　The [ext contains all the topics recommended by the National Science Foundation (NSF) sponsored Linear Algebra Curriculum Study Group (LACSG) and much more. Although there is more material than can be covered in a one-quarter or one-semester course, it is the author's feeling that it is easier for an instructor to leave out or skip material than it is to supplement a book with outside material. Even if many topics are omitted, the book should still provide students with a feeling for the overall scope of the subject matter. Furthermore, many students may use the book later as a reference and consequently may end up learning many of the omitted topics on theft own.
　　In the next section of this preface a number of outlines are provided for onesemester courses at either the sophomore level or the junior/senior level and with either a matrix-oriented emphasis or a slightly more theoretical emphasis. To further aid the instructor in the choice of topics, three sections have been designated as optional and are marked with an dagger in the table of contents. These sections are not prerequisites for any of the following sections in the book. They may be skipped without any loss of continuity.
　　Ideally the entire book could be covered in a two-quarter or two-semester sequence. Although two semesters of linear algebra has been recommended by the LACSG, it is still not practical at many universities and colleges. At present there is no universal agreement on a core syllabus for a second course. Indeed, if all of the topics that instructors would like to see in a second course were included in a single volume, it would be a weighty (and expensive) book. An effort has been made in this text to cover all of the basic linear algebra topics that are necessary for modem applications. Furthermore, two additional chapters for a second course are available for downloading from the Intemet. See the special Prentice Hall Web page discussed earlier. ...
　　Steven J. Leon
　　sleon@umassd.edu