Linear Algebra and Its Applications

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出版者:Pearson; 5 edition
作者:David C. Lay
出品人:
页数:576
译者:
出版时间:2015-1-3
价格:0
装帧:Hardcover
isbn号码:9780134022697
丛书系列:
图书标签:
  • 数学
  • 线性代数
  • LinearAlgebra
  • Algebra
  • 计算机基础
  • 数学-LinearAlgebra
  • Mathematics
  • textbook
  • 线性代数
  • 矩阵
  • 向量空间
  • 线性变换
  • 特征值
  • 特征向量
  • 解方程组
  • 应用数学
  • 高等数学
  • 数学
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具体描述

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 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.

目录信息

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

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)

读后感

评分

这周的作业有马尔科夫链和状态转移矩阵。最后变换为求解三元和四元的微分方程组的特解。 一类解法是拉普拉斯变换之后分离s和x(t),再使用逆变换。很不幸的是我功力尚浅,变换之后得到了一个满秩的齐次线性方程组。显然求解不下去。 另一种方法是矩阵的特征值和特征向量,相应的...  

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这是我发现的第三本台湾交大的使用教材。。和他们的OCourse相符。。。大家如果觉得看书太腻,就请结合一下台湾的OCourse视频来学吧。 网址:http://ocw.nctu.edu.tw/riki_detail.php?pgid=50&cgid=12 (不好意思,教材是有偏差,不過聽課還是幫助蠻大的,課程的順序也基本一樣)  

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001)143页,图2-23(c),说是【旋转-30度】,在图像却旋转了【90度】。――国际惯例,逆时针旋转为正方向,是这样的吧? 002)190页8行:“…,它们在【-比在】航天飞机中用到的数字系统中有用。”――这里疑似多了两个字符。 003)227页定理11的证明第2行:“若S生成H,则【...  

评分

这周的作业有马尔科夫链和状态转移矩阵。最后变换为求解三元和四元的微分方程组的特解。 一类解法是拉普拉斯变换之后分离s和x(t),再使用逆变换。很不幸的是我功力尚浅,变换之后得到了一个满秩的齐次线性方程组。显然求解不下去。 另一种方法是矩阵的特征值和特征向量,相应的...  

评分

在学习的同时,知道很多应用实例,记忆非常深刻。 学完这本书,对线性代数的应用可以到一定的广度的了解 但是学完国内一般的线性代数教材,觉得还是非常虚幻。强烈建议国内大学实用。  

用户评价

评分

后悔没有用这本书来入门,学习线代应该从直观的几何理解再到严谨抽象的代数概念。我的学习恰好反过来,数学系的高等代数严谨抽象,证明详细,对于入门来说,角度有些太高。这本书有着丰富的例子图像,以及线代在各个领域的实际应用,对于一些重要的定理也有粗略的证明,简直不要太棒!!

评分

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

评分

写的很好,概念非常清楚,非常好的入门和工具书,exercise也充足。但是prof没有讲完chapter7+8 ,还得补。(总成绩不是A系列……计算能力渣渣

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2019s1: 手里三本不同的线代教材,这本最好懂,一周目quiz靠自学第一章拿了满分,通读一遍拿hd我觉得不是问题。2019年7月3日:考的还是挺好的,但毕竟不是学校推荐教材,学校的课程outline不是按这本教材走的。pro:这本书第五章开篇举的那个关于猫头鹰population dynamics的例子。con:关于linear transformation的内容太少。

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非常适合初学和自学,看了1-8章和第10章,读这本书是一种享受,如听仙乐,绕梁三日,欲罢不能,可惜找不到第9章。

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