Linear Algebra and Its Applications

Linear Algebra and Its Applications pdf epub mobi txt 電子書 下載 2026

David C. Lay
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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)

具體描述

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.

用戶評價

評分

##????

評分

##非常適閤初學和自學,看瞭1-8章和第10章,讀這本書是一種享受,如聽仙樂,繞梁三日,欲罷不能,可惜找不到第9章。

評分

##看到好評如潮有點意外,算是終於得到一個例證吧。(題外話,怪不得教授怎麼講我都覺得不如看書好…………

評分

##綫性代數滾齣我的世界!!!——我對所有綫性代數一視同仁,不單單針對本書。夏校課裏記瞭44麵紙的筆記,其中34麵齣自於此。(Summer 2022)

評分

##用瞭大概90個小時伴著中文版讀完的,遇到中文版蹩腳的地方就讀原版這種 前五章打基礎,6-8章講瞭在實際過程中怎麼用,我缺的就是這塊知識,如果學數學隻是為瞭刷題,那這時間真不如打會兒遊戲 所以這本書,給瞭我學綫性代數的意義,自學一定要把原版也帶上!

評分

##2019s1: 手裏三本不同的綫代教材,這本最好懂,一周目quiz靠自學第一章拿瞭滿分,通讀一遍拿hd我覺得不是問題。2019年7月3日:考的還是挺好的,但畢竟不是學校推薦教材,學校的課程outline不是按這本教材走的。pro:這本書第五章開篇舉的那個關於貓頭鷹population dynamics的例子。con:關於linear transformation的內容太少。

評分

##這本書結構清晰,內容也全麵(該講的點在我看來都講瞭),所以很適閤本科生初學時作為主教材使用。唯一的遺憾就是課後習題瞭,有點過於偏重計算而忽視瞭理解,正文部分倒是沒這個問題,請放心閱讀。PS. 第一次學習時可以先跳過第四章

評分

##內容組織的非常好,難度循序漸進,清晰閤理,同時又有很多實際應用上的例子,讀起來非常的有趣。比國內那些垃圾綫代教材不知道高到哪裏去瞭。

評分

##非常適閤初學和自學,看瞭1-8章和第10章,讀這本書是一種享受,如聽仙樂,繞梁三日,欲罷不能,可惜找不到第9章。

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