Linear Algebra and Its Applications

出版者:Pearson; 5 edition

作者:David C. Lay

页数:576

出版时间:2015-1-3

价格:0

装帧:Hardcover

isbn号码:9780134022697

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

昨天在图书馆翻了翻"时间序列分析"的书，发现这东西还是很有用的，利用时间作为自变量来预测一个时间序列未来的值，比如，可以预测地震、天气、股票等等，由于它的自变量只有时间，所以感觉很神奇，几乎就是拿一个变量自己来做回归，称之为自回归AR（auto regression），另...  

看过了介绍后，感觉比较适合我。 本书是一本优秀的现代教材，给出最新的线性代数基本介绍和一些有趣应用。  

看过了介绍后，感觉比较适合我。 本书是一本优秀的现代教材，给出最新的线性代数基本介绍和一些有趣应用。  

04年上的大学，05年大二学习的概率论和线性代数，这两门课程学的差，考试也仅过及格线。当是完全不知道线性代数学来是干什么的。10年考研时接触到了统计，冥冥之中感觉统计的威力相当大，当事很想学习一下多元统计，翻开多元统计的书却发现完全看不懂，因为无所不在的线性代数...  

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）  

用户评价

这本《高等数学精要》简直是数学爱好者的福音，它的内容编排极为巧妙，将微积分、概率论和微分方程这三大数学支柱以一种令人耳目一新的方式串联起来。我过去总是觉得这些领域像是一座座孤立的山峰，各自为营，但这本书却搭建了精巧的桥梁。比如，它在讲解拉格朗日乘数法时，并没有直接跳入复杂的多元函数优化，而是先用一个简洁的概率模型来解释为何需要这种约束优化，这种代入感极强。再者，书中对级数展开的讨论非常深入，它不仅限于泰勒和麦克劳林，还花了大量篇幅探讨傅里叶级数在信号处理中的实际应用，配图详尽，即便没有深厚的工程背景也能大致领会其精髓。阅读过程中，我发现作者的语言风格极其富有感染力，像是老教授在课堂上与学生进行思维碰撞，而不是冷冰冰的公式堆砌。尤其是在介绍了一些经典难题的解法时，作者会先故意引导你尝试一种看似合理的错误路径，然后温柔地指出其中的逻辑谬误，这种“陪跑式”的教学方法，极大地提高了读者的自我修正能力。这本书的习题设计也堪称一绝，从基础的计算练习到开放性的探究问题，层次分明，让人感觉每做完一组练习，自己的思维深度就上了一个台阶。对于想要全面提升数学直觉和解决问题能力的理工科学生来说，这本书绝对是案头必备的宝典，它提供的不仅仅是知识点，更是一种思考的框架和视角。

我最近阅读的这本《后结构主义的解构：符号与权力》对于理解当代哲学思潮帮助极大，但它的阅读难度也是相当高的，需要极大的专注力。这本书的核心在于对传统“主体性”和“确定性意义”的颠覆性探讨。作者非常清晰地梳理了从索绪尔的结构主义到德里达和福柯等后结构主义思想家是如何一步步拆解语言、知识和权力之间相互建构的关系的。书中对“能指”和“所指”之间永远漂移的关系的论述极其透彻，它解释了为什么在后现代语境下，任何文本的意义都不再是固定和唯一的，而是在不断的“延迟”和“差异”中产生。更具启发性的是作者对“知识即权力”这一命题的深入剖析，他没有停留在表面的批判，而是通过对医学、监狱系统等机构话语的考察，展示了知识是如何被建构为一种社会控制的工具。这本书的论证结构非常严谨，大量引用了法语哲学家的原著，并附有详尽的注释，确保了观点的准确性，但这也意味着读者必须具备一定的哲学基础才能跟上作者的思路。这本书更像是一本“思想的健身房”，它强迫你去质疑你习以为常的一切认知边界，读完后，我看待新闻报道、官方声明的方式都发生了一种微妙的、却又根本性的转变。

《古代密码学原理与应用》这本书，简直是一把开启神秘历史大门的钥匙。我原本对密码学仅停留在二战中恩尼格玛机（Enigma）的印象，但这本书将历史的跨度拓展到了古代文明的通讯加密实践。作者的叙事方式非常引人入胜，他不是简单地罗列算法，而是将每个密码系统的出现都置于其特定的历史背景中去考量。例如，书中对斯巴达的“丝带密码”（Scytale）的讨论，不仅展示了其原理——一个简单的圆柱转轴——还详细描述了在战场通讯中，如何通过快速缠绕和解缠绕来确保信息的秘密传递，体现了古人对物理形态安全性的巧妙利用。随后，作者过渡到凯撒密码和更复杂的替换密码时，采用了“挑战与应对”的叙事结构，每一次新的加密方法的出现，都伴随着解密者（如阿尔-金迪）所使用的频率分析等新技术的诞生。书中对不同文明在密码学上的侧重点也有独到的见解，比如波斯人在信息安全与情报传递上的高屋建瓴，与古罗马人在军事信号灯系统上的工程实用主义形成了有趣的对比。最让我叫绝的是，书中穿插了一些可供读者动手的“小实验”，比如用手边的纸和笔就可以模拟一些简单的转位密码，这让抽象的数学概念瞬间变得具体可感，体验感极佳。

《气候变化与生态系统响应》这本书，给我带来的震撼主要来自于其数据的详实和模型的精妙。我原本以为关于气候的书籍大多会充斥着耸人听闻的预测，但这本书的基调却是冷静、严谨且基于实证的。作者团队显然投入了巨大的精力进行跨学科整合，他们不仅展示了大气环流模型的最新进展，还非常细致地剖析了特定生物群落对温度和海洋酸化的反应。例如，书中有一章专门讨论了珊瑚礁白化的过程，它将化学反应速率、光合作用效率降低与区域洋流变化的数据模型做了精确的叠合，而非简单地归咎于“水温升高”。更让我印象深刻的是其对“临界点”概念的探讨。作者没有给出模糊的“全球变暖阈值”，而是通过一系列复杂的反馈回路图，展示了不同生态系统（如西伯利亚永久冻土层和亚马逊雨林）各自具有的、可能导致不可逆转变化的内部驱动机制，这种分层级的分析，比笼统的“末日论”更具警示性和教育意义。这本书的图表绘制达到了教科书级别的标准，每一个散点图、热力图都清晰地标注了其数据源和误差范围，这对于需要进行批判性思考的读者来说，是极大的帮助。读完后，我对“生态平衡”的理解不再是教科书上的简单定义，而是理解为一个在多重压力下不断进行动态调整的、极其脆弱的复杂系统。

翻开《世界文学的瑰宝》，我立刻被那种扑面而来的文学气息所吸引。这本书的选材极其宏大，它不拘泥于单一的语种或地域，而是以时间为轴线，精选了从荷马史诗的残篇到后现代主义的意识流小说片段，进行了一次跨越千年的文学漫步。这本书的精彩之处在于它的“解读”部分，作者似乎拥有“穿透文本的魔力”。对于《堂吉诃德》的分析，他没有停留在骑士精神的讽刺层面，而是深入探讨了“理想与现实的永恒张力”如何在不同历史时期被不同文化背景下的作家所重塑，这种比较文学的视角让人豁然开朗。此外，书中对不同文学流派的风格演变也做了细致的剖析，比如浪漫主义时期对“崇高”的追求如何与现代主义对“碎片化”的迷恋形成鲜明对比，并配有大量原著的对照翻译，使得即使是不太接触原版文学的读者也能清晰感知其语言风格的巨大差异。这本书的排版和装帧也充满了艺术感，纸张的质地、字体的选择，都透露出对文学作品应有的尊重。它更像是一本“文学鉴赏的入门向导”，而非枯燥的理论教材。读完它，你不会觉得文学是高高在上的殿堂，而是遍布生活各个角落、充满生命力的叙事艺术。它成功地激发了我重新阅读那些被遗忘的经典作品的冲动，因为我突然明白了，那些文字背后蕴含的，是人类最深层的欲望和困惑。

第一章基本读的它，后来转第四版了。但附录不错，有空学学说到的matlab。

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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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内容组织的非常好，难度循序渐进，清晰合理，同时又有很多实际应用上的例子，读起来非常的有趣。比国内那些垃圾线代教材不知道高到哪里去了。