基本信息
- 原书名：Linear Algebra with Applications，Sixth Edition
- 原出版社： Prentice Hall/Pearson
- 作者： （美）Steven J.Leon
- 丛书名： 经典原版书库
- 出版社：机械工业出版社
- ISBN：9787111152163
- 上架时间：2004-10-22
- 出版日期：2004 年10月
- 开本：16开
- 页码：544
- 版次：6-1
- 所属分类：数学 > 代数，数论及组合理论 > 线性代数
教材
内容简介
书籍
数学书籍
随着计算机技术的发展，线性代数课程的重要性越来越突出。同时，现代软件已经使显著改善授课方式成为可能。本书作者多年讲授线性代数课程，并在教学过程中不断探索更利于学生理解的新教学方法，从而使本书更加适合作为线性代数课程的教材。
本书主要包括矩阵与方程组、行列式、向量空间、线性变换、正交性、特征值、迭代法和若尔当标准型等内容。
本书的主要特点：
●通过大量的实际应用说明了线性代数在各个领域中的广泛应用。
●包含许多示例，便于读者理解相关的定义及原理。
●每一节的后面给出大量的习题，各章后面还有测试题，并在本书的最后提供了部分习题的答案。
●每章的后面都有基子MALAB的上机练习，并在附录中提供了MALAB的基础知识。
数学书籍
随着计算机技术的发展，线性代数课程的重要性越来越突出。同时，现代软件已经使显著改善授课方式成为可能。本书作者多年讲授线性代数课程，并在教学过程中不断探索更利于学生理解的新教学方法，从而使本书更加适合作为线性代数课程的教材。
本书主要包括矩阵与方程组、行列式、向量空间、线性变换、正交性、特征值、迭代法和若尔当标准型等内容。
本书的主要特点：
●通过大量的实际应用说明了线性代数在各个领域中的广泛应用。
●包含许多示例，便于读者理解相关的定义及原理。
●每一节的后面给出大量的习题，各章后面还有测试题，并在本书的最后提供了部分习题的答案。
●每章的后面都有基子MALAB的上机练习，并在附录中提供了MALAB的基础知识。
作译者
Steven J．Leon 1971年于密歇根州立大学数学系获得博士学位。现为马萨诸塞大学达特茅斯分校数学系首席教授，ILAS(国际线性代数协会)、MAA(美国数学学会)和SIAM(美国工业与应用数学协会)成员。他主要从事科学计算、线性代数和应用数学等领域的研究。
目录
PREFACE iv
1 MATRICES AND SYSTEMS OF EQUATIONS
1 Systems of Linear Equations 1
2 Row Echelon Form 13
3 Matrix Algebra 33
4 Elementary Matrices 67
5 Partitioned Matrices 79
MATLAB Exercises 91
Chapter Test 97
2 DETERMINANTS 99
1 The Determinant ora Matrix 99
2 Properties of Determinants 107
3 Cramer's Rule 115
MATLAB Exercises 121
Chapter Test 123
3 VECTOR-SPACES 125
1 Definition and Examples 125
2 Subspaces 134
3 Linear Independence 144
4 Basis and Dimension 156
1 MATRICES AND SYSTEMS OF EQUATIONS
1 Systems of Linear Equations 1
2 Row Echelon Form 13
3 Matrix Algebra 33
4 Elementary Matrices 67
5 Partitioned Matrices 79
MATLAB Exercises 91
Chapter Test 97
2 DETERMINANTS 99
1 The Determinant ora Matrix 99
2 Properties of Determinants 107
3 Cramer's Rule 115
MATLAB Exercises 121
Chapter Test 123
3 VECTOR-SPACES 125
1 Definition and Examples 125
2 Subspaces 134
3 Linear Independence 144
4 Basis and Dimension 156
前言
The author is pleased to see the text reach its sixth edition. While the continued support and enthusiasm of the many users has been most gratifying, this does not mean that a mild revision is in order. Linear algebra is more exciting now than at almost any time in the past. Its applications continue to spread to more and more fields. Largely due to the computer revolution of the last half century, linear algebra has risen to a role of prominence in the mathematical curriculum rivaling that of calculus. Modern software has also made it possible to dramatically improve the way the course is taught. The author teaches linear algebra every semester and continues to seek new ways to optimize student understanding. For this edition every chapter has been carefully scrutinized and enhanced. Additionally, many of the revisions in this edition are due to the helpful suggestions received from users and reviewers. Consequently, this new edition, while retaining the essence of previous editions, incorporates a wide array of substantive improvements.
WHAT'S NEW IN THE SIXTH EDITION?
1. Chapter Tests
New to this edition are chapter tests. At the end of each chapter there is a true-false exam testing the basic concepts covered in the chapter. Students are asked to prove or explain all of their answers.
2. Earlier Presentation of the Singular Value Decomposition
The singular value decomposition (SVD) has emerged as one of the most important tools in matrix applications. Unfortunately, the topic is often omitted from linear algebra textbooks. When covered, it usually appears near the end of the book and classes rarely have time to get that far. To remedy this, we have moved the singular value decomposition approximately 100 pages forward in the book. It is now covered in Section 5 of Chapter 6. In this section we also show the applications of the singular value decomposition to least squares problems, principal component analysis, information retrieval, numerical rank of a matrix, and digital imaging. The SVD section nicely ties together some of the major topics, such as fundamental subspaces, orthogonality, and eigenvalues. It provides an ideal climax to a linear algebra course.
3. New and Improved Applications
Eight applications were added to the previous edition. Some of these have been revised and improved in the current edition. A number of new applications have also been added. In Chapter 1 we show how matrices are used for search engines and information retrieval applications. This application is revisited in Chapters 5 and 6 after students have learned about orthogonality and singular values. Similarly, the statistical applications in Chapter 5 are revisited later in Chapter 6 after students have learned about the singular value decomposition.
4. New Computer Exercises Emphasizing Visualization
Chapter 6 has ten new MATLAB exercises to help students to visualize eigen values and singular values and to help them gain geometric insight into these subjects.
5. New and Improved Examples
Worked out examples make the textbook seem less abstract and more user friendly. Often students don't understand what a theorem says until they see a worked out example that illustrates the theorem. The impressive collection of examples was often cited as one of the strong points of the first edition of this book. This collection has continued to grow and improve with each new edition. More examples have been added throughout the sixth edition, and many of the previous examples have been revised and improved. Now, for example, the numbered of worked out examples in Chapter 1 has increased from 32 to 34. In a number of cases color shading is now used to emphasize how rows and columns are paired off in matrix computations.
6. New Theorem and Improved Nomenclature
Throughout this edition we have made a special effort to assign names to theorems so as to emphasize the importance of the results. Also, it is easier to refer back to a theorem if it has a name. We have added a new theorem to Chapter 6. This theorem does have a name, The Principal Axes Theorem.
7. Revised Organization of Chapter 5
In Chapter 5 the order of two of the sections has been reversed. Least squares problems are now covered before the section on general inner product spaces. To facilitate this change, some new material was added to Section 1 of the chapter. With this new ordering it is possible for classes that only treat Euclidean vector spaces to skip most of Section 4. These classes need only introduce the inner product notation in Section 4 and then move on to the next section or, if pressed for time, skip ahead to the next chapter.
8. New Subsection on Outer Products
A new subsection on-outer product expansions has been added to Chapter 1. Outer product expansions are used in later chapters applications such as digital imaging.
9. Special Web Site and Supplemental Web Materials
Prentice Hall has developed a special Web site to accompany this book. This site includes a host of materials for both students and instructors. The Web pages are being extensively revised for the sixth edition and an exciting collection of new interactive course materials is currently being developed as we go to press. Some of the other features to be included on the Web pages are a collection of links with downloadable materials relating to each of the chapters in the book and a collection of application projects that are related to the topics covered in the book. You can also download two supplemental chapters for this book from the Prentice Hall site. The new chapters are:
WHAT'S NEW IN THE SIXTH EDITION?
1. Chapter Tests
New to this edition are chapter tests. At the end of each chapter there is a true-false exam testing the basic concepts covered in the chapter. Students are asked to prove or explain all of their answers.
2. Earlier Presentation of the Singular Value Decomposition
The singular value decomposition (SVD) has emerged as one of the most important tools in matrix applications. Unfortunately, the topic is often omitted from linear algebra textbooks. When covered, it usually appears near the end of the book and classes rarely have time to get that far. To remedy this, we have moved the singular value decomposition approximately 100 pages forward in the book. It is now covered in Section 5 of Chapter 6. In this section we also show the applications of the singular value decomposition to least squares problems, principal component analysis, information retrieval, numerical rank of a matrix, and digital imaging. The SVD section nicely ties together some of the major topics, such as fundamental subspaces, orthogonality, and eigenvalues. It provides an ideal climax to a linear algebra course.
3. New and Improved Applications
Eight applications were added to the previous edition. Some of these have been revised and improved in the current edition. A number of new applications have also been added. In Chapter 1 we show how matrices are used for search engines and information retrieval applications. This application is revisited in Chapters 5 and 6 after students have learned about orthogonality and singular values. Similarly, the statistical applications in Chapter 5 are revisited later in Chapter 6 after students have learned about the singular value decomposition.
4. New Computer Exercises Emphasizing Visualization
Chapter 6 has ten new MATLAB exercises to help students to visualize eigen values and singular values and to help them gain geometric insight into these subjects.
5. New and Improved Examples
Worked out examples make the textbook seem less abstract and more user friendly. Often students don't understand what a theorem says until they see a worked out example that illustrates the theorem. The impressive collection of examples was often cited as one of the strong points of the first edition of this book. This collection has continued to grow and improve with each new edition. More examples have been added throughout the sixth edition, and many of the previous examples have been revised and improved. Now, for example, the numbered of worked out examples in Chapter 1 has increased from 32 to 34. In a number of cases color shading is now used to emphasize how rows and columns are paired off in matrix computations.
6. New Theorem and Improved Nomenclature
Throughout this edition we have made a special effort to assign names to theorems so as to emphasize the importance of the results. Also, it is easier to refer back to a theorem if it has a name. We have added a new theorem to Chapter 6. This theorem does have a name, The Principal Axes Theorem.
7. Revised Organization of Chapter 5
In Chapter 5 the order of two of the sections has been reversed. Least squares problems are now covered before the section on general inner product spaces. To facilitate this change, some new material was added to Section 1 of the chapter. With this new ordering it is possible for classes that only treat Euclidean vector spaces to skip most of Section 4. These classes need only introduce the inner product notation in Section 4 and then move on to the next section or, if pressed for time, skip ahead to the next chapter.
8. New Subsection on Outer Products
A new subsection on-outer product expansions has been added to Chapter 1. Outer product expansions are used in later chapters applications such as digital imaging.
9. Special Web Site and Supplemental Web Materials
Prentice Hall has developed a special Web site to accompany this book. This site includes a host of materials for both students and instructors. The Web pages are being extensively revised for the sixth edition and an exciting collection of new interactive course materials is currently being developed as we go to press. Some of the other features to be included on the Web pages are a collection of links with downloadable materials relating to each of the chapters in the book and a collection of application projects that are related to the topics covered in the book. You can also download two supplemental chapters for this book from the Prentice Hall site. The new chapters are:
