出版社: Pearson
出版年: 2011-1-20
页数: 576
定价: USD 207.60
装帧: Hardcover
ISBN: 9780321385178
内容简介 · · · · · ·
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easil...
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick 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. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete R n setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.
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. 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 ...
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. 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 over 30 research articles published in functional analysis and linear algebra.
As a founding member of the NSF-sponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also co-author 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.
Professor 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. 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.
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: Readjusting the North American Datum
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: Google and Markov Chains
10.1 Introduction and Examples
10.2 The Steady-State Vector and Google's PageRank
10.3 Finite-State Markov Chains
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
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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
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订阅关于Linear Algebra and Its Applications的评论:
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0 有用 Loy 2015-08-14 10:33:52
大学时候读的,是读过的第一本英文书。
0 有用 灵昭 2021-01-18 07:20:32
Linear algebra. Dec 2020.
0 有用 Snjór 2018-01-02 08:57:44
sheer transformation
0 有用 蘅初 2014-02-08 00:22:43
看了一下价钱吓尿了
1 有用 地下宇航员 2014-01-30 17:00:02
太水了,不够用。想读经济研究生的还得另补
0 有用 绿野 2023-05-31 06:54:55 美国
这本对我很友好,但是考试太不友好呜。
0 有用 灵昭 2021-01-18 07:20:32
Linear algebra. Dec 2020.
0 有用 momo 2020-07-23 11:56:02
do ppl really read books to learn maths tho...
0 有用 nobody 2020-05-08 09:00:44
写得挺好的线性代数的一本书,里面也提到了很多实际的应用
0 有用 楼霸 2020-04-23 16:14:03
线代入门强烈推荐!!!虽然考研数学高分飘过,但是感觉自己并没有理解线性代数,只是会机械的进行解题。可能这也是国内工科教育的通病。这种情况会导致后期在进行应用时出现抓瞎的情况,无法将实际情况与理论联系。由于在项目中遇到了图像空间变换的问题,发现很多概念无法清晰理解,所以想找一本线代书籍回顾相关概念。在知乎看见了这本书的推荐。从Ax=b的基本概念触发,到vector space,再到optimizat... 线代入门强烈推荐!!!虽然考研数学高分飘过,但是感觉自己并没有理解线性代数,只是会机械的进行解题。可能这也是国内工科教育的通病。这种情况会导致后期在进行应用时出现抓瞎的情况,无法将实际情况与理论联系。由于在项目中遇到了图像空间变换的问题,发现很多概念无法清晰理解,所以想找一本线代书籍回顾相关概念。在知乎看见了这本书的推荐。从Ax=b的基本概念触发,到vector space,再到optimization,真正让我见识了线代作为工具的巨大作用。里面与工程应用(微分方程、空间变换、最优化)的结合更是把以前学过的工科知识串联起来,有一种醍醐灌顶的感觉。一天一章,差不多半个月看完,这种通透的感觉太爽了!!! (展开)