出版社: Pearson; 5 edition
出版年: 2015-1-3
页数: 576
装帧: Hardcover
ISBN: 9780134022697
内容简介 · · · · · ·
With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) a...
With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand.
作者简介 · · · · · ·
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 Universi...
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.
目录 · · · · · ·
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
· · · · · · (更多)
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 Communication Classes
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
· · · · · · (收起)
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Linear Algebra and Its Applications的书评 · · · · · · ( 全部 49 条 )
挺好的 看完后对LA建立起了基本概念
> 更多书评 49篇
论坛 · · · · · ·
感觉这本书的一些定义并不严谨 | 来自WONDON | 2023-10-16 13:30:47 |
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订阅关于Linear Algebra and Its Applications的评论:
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0 有用 Turin Horse 2023-06-25 09:18:17 北京
好教材 国内线代教材完全比不了
0 有用 夕立 2022-08-10 10:32:17
线性代数滚出我的世界!!!——我对所有线性代数一视同仁,不单单针对本书。夏校课里记了44面纸的笔记,其中34面出自于此。(Summer 2022)
0 有用 匿明用户 2021-03-10 13:14:35
疫情期间懒得看录播就只看书自学也能理解完全的书…给的例子真好啊…15天过完6个chapter还是太恐怖了…让我Block Break的时候再慢慢读完它
0 有用 ABCD 2019-08-25 18:53:50
最后一章写的太简略了,不过也毕竟这本书是一线性代数为主
2 有用 花开花落她是谁 2018-05-12 05:22:32
看到好评如潮有点意外,算是终于得到一个例证吧。(题外话,怪不得教授怎么讲我都觉得不如看书好…………
0 有用 未见青山老 2024-03-25 13:35:31 山东
学这本的效果一般....当时好多地方反复犯错,反复想不明白,比如R²没有mulplication....
0 有用 Turin Horse 2023-06-25 09:18:17 北京
好教材 国内线代教材完全比不了
0 有用 pota头 2023-05-15 12:37:12 甘肃
我啃完的第一本英文学术原著,但居然比翻译版还要好读得多,翻译版真垃圾。原书很好懂,掌握一些术语单词后,不难理解
0 有用 夕立 2022-08-10 10:32:17
线性代数滚出我的世界!!!——我对所有线性代数一视同仁,不单单针对本书。夏校课里记了44面纸的笔记,其中34面出自于此。(Summer 2022)
0 有用 黄色失眠小马 2021-07-08 15:55:29
用了大概90个小时伴着中文版读完的,遇到中文版蹩脚的地方就读原版这种 前五章打基础,6-8章讲了在实际过程中怎么用,我缺的就是这块知识,如果学数学只是为了刷题,那这时间真不如打会儿游戏 所以这本书,给了我学线性代数的意义,自学一定要把原版也带上!