线性代数
作者：杨文霞，向建林著
出版时间：2017年版
内容简介
《线性代数》是针对双语教学及来华留学生英语教学而编写的线性代数英文教材。《线性代数》对线性代数的内容作了比较准确的、深入浅出的英文表述。内容包括行列式、矩阵、向量、线性方程组、矩阵的特征值与特征向量、矩阵的相似对角化、二次型及其标准形等。数学专业表述及技术符号系统与国际现行教学规范一致。教材每个章节配备了习题并附有参考答案。《线性代数》适合作为我国高等院校同名课程的双语教学及来华留学生英文教学的配套教材，也可以作为英语专业的数学课程的教科书，以及数学与应用数学、信息与计算科学专业学科英语的阅读参考书。
目录
Chapter 1 Systems of Linear Equations and Elementary Operations on Matrices
1．1 Systems of Linear Equations
1．1．1 Definition
1．1．2 Equivalent Systems and Gaussian Elimination Method
Exercises 1．1
1．2 Elementary Operations on Matrices
1．2．1 Elementary Row Operations
1．2．2 Row Echelon Forms
1．2．3 Standard Form of a Matrix
Exercises 1．2
Chapter 2 Determinants
2．1 The Determinant of a Matrix
2．1．1 Determinants of order 2 and order 3
2．1．2 Permutations and Number of Inversions
2．1．3 Determinant of an nXn Matrix
Exercises2．1
2．2 Properties of Determinants
Exercises2．2
2．3 The Cofactor Expansion of a Determinant
Exercises2．3
2．4 Cramer's Rule
Exercises 2．4
Chapter 3 Matrices Algebra
3．1 Matrices Arithmetic
3．1．1Matrices
3．1．2Matrix Addition
3．1．3 Scalar Multiplication
3．1．4 Matrix Multiplication
3．1．5 Powcrs of a Square Matrix
Exercise 3．1
3．2Special Matrices
3．2．1The Identity Matrix
3．2．2 The DiagonalMatrix
3．2．3 Triangular Matrices
3．2．4 The Transpose of a Matrix
3．2．5 Symmetric and Skew-Symmetric Matriccs
3．2．6The Determinant of the Product AB
3．2．7 Adjoint ofa Matrix
Exercises 3．2
3．3 The Inverse of a Mtrix
3．3．1 Thelnverse of a Matrix
3．3．2Properties of Invertible Matrices
Exercises 3．3
3．4 Partitioned Matrices
3．4．1 Partitioned Matrices
3．4．2Operations on Partitioned Matrices
Exercises 3．4
3．5 Elementary Matrices
3．5．1 Elementary Matrices
3．5．2Theorems of Invertible Matrices
3．5．3 Computing the Inverse by Elementary Row Operations
3．5．4 Solving Matrix Equations by Elementary Row Operations
Exercises 3．5
3．6 The Rank of a Matrix
3．6．1 The Rank of a Matrix
3．6．2 Properties of the Ranks of Matrices
Exercises 3．6
Chapter 4 Structure of Solutions for Systems of Linear Equations
Chapter 5 Similar Matrices and Quadratic Forms
Answers to Exercises
References
