線性代數（簡體書）

《Linear Algebra》是在教育部大力推進雙語教學的大背景下推出的，結合當前開展線性代數課程雙語教學的實際情況，以教育部數學與統計學教學指導委員會制定的本課程教學基本要求為依據，同時兼顧線性代數的研究生入學統一考試大綱要求，該書的中文版為同名作者編寫的普通高等教育“十一五”國家級規劃教材。與中文版一樣，英文版教材突出現代代數學和離散數學的思想，著重講解線性代數的基本概念、基本理論和基本方法，尤其注重體現線性代數在各個領域中的廣泛應用，將大量的相關實例融合貫穿于理論、方法的講解中，將經典和現代代數學的思想與離散數學的方法闡述得更為具體、實用。
《Linear Algebra》內容包括線性代數方程組、矩陣、行列式、矩陣的秩和線性方程組的解、向量空間初步、矩陣的特徵值問題和線性變換等共7章。全書取材的深廣度合適，注重聯系應用，強調數學建模的融入，符合大學本科教學對本門課程的教學要求與實際需要。《Linear Algebra》的起點較低、知識系統、詳略得當、舉例豐富、講解透徹、難度適宜、思路清晰、易教易學，有利于培養學生用線性代數的思維方法去分析問題、解決問題，并注意激發學生學習的興趣和主動性。
英文版教材邀請了在美國任教的華裔學者共同編寫、審定，在文字表述方面，英文語言簡單易懂，寫作風格簡約，可供普通高等學校工科類、理科類（非數學專業）、經濟管理類有關專業的線性代數課程雙語教學使用。

Chapter 1 System of Linear Equations and Elimination Method
1.1 Solving System of Linear Equations with Elimination Method
1.1.1 Linear System with Two Unknowns
1.1.2 Gauss-Jordan Elimination Method
1.2 Applications
Practice 1

Chapter 2 Matrices
2.1 Basic Concepts
2.1.1 Matrices
2.1.2 Special Matrices
2.1.3 Problems Related to Matrices
2.2 Basic Operations
2.2.1 Definitions
2.2.2 Rules of Operations
2.2.3 Applications
2.3 Matrix Inverses
2.3.1 lnvertible Matrices
2.3.2 Orthogonal Matrices
2.4 Blocks and Sub-matrices
2.4.1 Block Operations
2.4.2 Column Blocks
2.4.3 Sub-matrices
2.5 Elementary Operations and Elementary Matrices
2.5.1 Definitions and Properties
2.5.2 Equivalent Normal Form for Matrices
2.5.3 Invertible Matrices Revisit
2.5.4 Unique solution for n x n linear systems
2.6 Applications(Input - output Analysis)
Practice 2

Chapter 3 Determinants
3.1 Definitions and Properties of Determinants
3.1.1 Definitions
3.1.2 Propertie
3.2 Evaluation of Determinants
3.3 Applications
3.3.1 Adjugate Matrices and Inverse Formula
3.3.2 Cramer's Rule
3.3.3 Summary
Practice 3

Chapter 4 Rank of a Matrix and Solutions for Linear Systems
4.1 Rank of a Matrix
4.1.1 Concepts
4.1.2 Computations
4.2 Solutions of Linear Systems
4.2.1 Homogeneous Systems
4.2.2 Non-homogeneous Systems
Practice 4

Chapter 5 Vector Spaces
5.1 Concepts
5.2 Linear Dependence and Linear Independence
5.2.1 Concepts
5.2.2 Properties
5.2.3 Rank of a Set of Vectors
5.2.4 Row and Column Ranks of a Matrix
5.3 Bases and Dimensions of Vector Spaces
5.3.1 Bases and Dimensions
5.3.2 Revisit Solutions for Linear Systems
5.4 Inner Products
5.4.1 Review
5.4.2 Inner Products and Orthogonal Matrices
5.4.3 Four Basic Subspaces
Practice 5

Chapter 6 Eigenvalues
6.1 Eigenvalues and Eigenvectors
6.2 Diagonalizations'
6.2.1 Similar Matrices and Diagonal Forms
6.2.2 Applications
6.3 Real Symmetric Matrices and Quadratic Forms
6.3..1 Canonical Forms for Real Symmetric Matrices
6.3.2 Quadratic Forms
6.3.3 Quadratic Expressions and Their Canonical Forms
6.4 Positive Definite Matrices and Classification of Quadratic Forms
6.4.1 Positive Definite Matrices
6.4.2 Optimization
6.4.3 Generalized Eigenvalue Problems
Practice 6

Chapter 7 Linear Transformations
7.1 Basic Concepts of Linear Transformations
7.1.1 Linear Transformations
7.1.2 Range and Kernel for a Linear Transformation
7.2 Linear Transformations and Matrices
7.2.1 Coordinate Vectors
7.2.2 The Matrix Representations for Linear Transformations
7.2.3 Engenvalues and Eigenvectors of a Linear Transformation
Practice 7
References