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)
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.
用户评价
##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
##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。
##由于时间和精力，只做了PRACTICE PROBLEMS部分，EXERCISES只挑了几题做。书中的第9章和10章是网络上的章节，可惜原书并未收录，所以只是看看章节名而已。 不过也是从头到尾翻了一遍，这确实是本好书，甩国内绝大部分教材几条街，至此也是重新学了下线性代数了。
##😂
##前7章打基础，第8/9/10三个章节需要重点反复读，当然内容并不基础。
##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。
##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。
##Read it for some note on singular value decomposition, yet another mediocre textbook with unclear constructure.
##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