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线性代数=Linear-Algebra:英文


毛纲源,马迎秋,梁敏 著

    

发表于2020-07-15

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出版社: 华中科技大学出版社
ISBN:9787568028288
版次:1
商品编码:12248389
包装:平装
丛书名: 普通高等教育“十三五”规划教材 普通高等院校数学精品教材
开本:16开
出版时间:2017-12-01
用纸:胶版纸
页数:280
字数:370000
正文语种:中文

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具体描述

编辑推荐

适读人群 : 高等院校理工、财经、医药、农林等专业大学本科生、研究生,从事线性代数双语或英语教学的教师,特别是准备出国留学的大学生及高中毕业生
本书可以作为大学数学线性代数双语或英语教学教师和准备出国留学深造学子的参考书。特别适合中外合作办学的国际教育班的学生,能帮助他们较快地适应全英文的学习内容和教学环境,完成与国外大学学习的衔接。本书在定稿之前已在多个学校作为校本教材试用,而且得到了师生的好评。

内容简介

本书采用学生易于接受的知识结构方式和英语表述方式,科学、系统地介绍了线性代数的行列式、矩阵、高斯消元法解线性方程组、向量、方程组解的结构、特征值和特征向量、二次型等知识。强调通用性和适用性,兼顾先进性。本书起点低,难度坡度适中,语言简洁明了,不仅适用于课堂教学使用,同时也适用于自学自习。全书有关键词索引,习题按小节配置,题量适中,题型全面,书后附有答案。
本书读者对象为高等院校理工、财经、医药、农林等专业大学生和教师,特别适合作为中外合作办学的国际教育班的学生以及准备出国留学深造学子的参考书。

作者简介

毛纲源,武汉理工大学资深教授,毕业于武汉大学,留校任教,后调入武汉工业大学(现合并为武汉理工大学)担任数学物理系系主任,在高校从事数学教学与科研工作40余年,除了出版多部专著(早在1998年,世界科技出版公司World Scientific Publishing Company就出版过他主编的线性代数Linear Algebra的英文教材)和发表数十篇专业论文外,还发表10余篇考研数学论文。
主讲微积分、线性代数、概率论与数理统计等课程。理论功底深厚,教学经验丰富,思维独特。曾多次受邀在各地主讲考研数学,得到学员的广泛认可和一致好评:“知识渊博,讲解深入浅出,易于接受”“解题方法灵活,技巧独特,辅导针对性极强”“对考研数学的出题形式、考试重点难点了如指掌,上他的辅导班受益匪浅”。
马迎秋,北京师范大学珠海分校副教授,毕业于渤海大学,爱尔兰都柏林大学数学硕士。主讲微积分、线性代数、数学教学论、数学教学设计、数学史与数学文化等课程。在国内外权wei期刊发表中英文论文10余篇。
梁敏,北京师范大学珠海分校副教授,毕业于天津大学,美国托莱多大学数学硕士,美国罗格斯大学统计学硕士。主讲微积分、线性代数、概率论与数理统计、商务统计、运筹学等课程。在国内外权wei期刊发表中英文论文10余篇。

精彩书评

本书是线性代数教材,采用全英文编写,是作者几十年来在教学一线工作经验的总结,在编写过程中参考了国外优秀的英语线性代数教材,探讨了适应中国学生学习的一些内容和模式,符合当前大学数学线性代数课程英语教学的特点,很具有实用性和针对性。

目录

Chapter 1 Determinant(1)
1.1 Definition of Determinant(1)
1.1.1 Determinant arising from the solution of linear system(1)
1.1.2 The definition of determinant of order n(5)
1.1.3 Determine the sign of each term in a determinant (8)
Exercise 1.1(10)
1.2 Basic Properties of Determinant and Its Applications(12)
1.2.1 Basic properties of determinant(12)
1.2.2 Applications of basic properties of determinant(15)
Exercise 1.2(19)
1.3 Expansion of Determinant (21)
1.3.1 Expanding a determinant using one row (column)(21)
1.3.2 Expanding a determinant along k rows (columns)(27)
Exercise 1.3(29)
1.4 Cramer’s Rule(30)
Exercise 1.4(36)

Chapter 2 Matrix(38)
2.1 Matrix Operations(38)
2.1.1 The concept of matrices(38)
2.1.2 Matrix Operations(41)
Exercise 2.1(58)
2.2 Some Special Matrices(60)
Exercise 2.2(64)
2.3 Partitioned Matrices(66)
Exercise 2.3(72)
2.4 The Inverse of Matrix(73)
2.4.1 Finding the inverse of an n×n matrix(73)
2.4.2 Application to economics(81)
2.4.3 Properties of inverse matrix (83)
2.4.4 The adjoint matrix A�� (or adjA) of A(86)
2.4.5 The inverse of block matrix(89)
Exercise 2.4(91)
2.5 Elementary Operations and Elementary Matrices(94)
2.5.1 Definitions and properties (94)
2.5.2 Application of elementary operations and elementary matrices(100)
Exercise2.5(102)
2.6 Rank of Matrix(103)
2.6.1 Concept of rank of a matrix(104)
2.6.2 Find the rank of matrix(107)
Exercise 2.6(109)

Chapter 3 Solving Linear System by Gaussian Elimination Method(110)
3.1 Solving Nonhomogeneous Linear System by Gaussian Elimination Method(110)
3.2 Solving Homogeneous Linear Systems by Gaussian Elimination Method(128)
Exercise 3(131)

Chapter 4 Vectors(134)
4.1 Vectors and its Linear Operations(134)
4.1.1 Vectors(134)
4.1.2 Linear operations of vectors(136)
4.1.3 A linear combination of vectors (137)
Exercise 4.1(143)
4.2 Linear Dependence of a Set of Vectors (143)
Exercise 4.2(155)
4.3 Rank of a Set of Vectors(156)
4.3.1 A maximal independent subset of a set of vectors(156)
4.3.2 Rank of a set of vectors(159)
Exercise 4.3(163)

Chapter 5 Structure of Solutions of a System(165)
5.1 Structure of Solutions of a System of Homogeneous Linear Equations (165)
5.1.1 Properties of solutions of a system of homogeneous linear equations(165)
5.1.2 A system of fundamental solutions (166)
5.1.3 General solution of homogeneous system(171)
5.1.4 Solutions of system of equations with given solutions of the system(173)
Exercise 5.1(176)
5.2 Structure of Solutions of a System of Nonhomogeneous Linear Equations(178)
5.2.1 Properties of solutions(178)
5.2.2 General solution of nonhomogeneous equations (179)
5.2.3 The simple and convenient method of finding the system of fundamental solutions and particular solution(183)
Exercise 5.2(189)

Chapter 6 Eigenvalues and Eigenvectors of Matrices(191)
6.1 Find the Eigenvalue and Eigenvector of Matrix(191)
Exercise 6.1(197)
6.2 The Proof of Problems Related with Eigenvalues and Eigenvectors(198)
Exercise 6.2(199)
6.3 Diagonalization(200)
6.3.1 Criterion of diagonalization(200)
6.3.2 Application of diagonalization(209)
Exercise 6.3(210)
6.4 The Properties of Similar Matrices(211)
Exercise 6.4(216)
6.5 Real Symmetric Matrices(218)
6.5.1 Scalar product of two vectors and its basis properties(218)
6.5.2 Orthogonal vector set(220)
6.5.3 Orthogonal matrix and its properties(223)
6.5.4 Properties of real symmetric matrix(225)
Exercise 6.5(229)

Chapter 7 Quadratic Forms (231)
7.1 Quadratic Forms and Their Standard Forms(231)
Exercise 7.1(236)
7.2 Classification of Quadratic Forms and Positive Definite Quadratic(Positive Definite Matrix)(237)
7.2.1 Classification of Quadratic Form(237)
7.2.2 Criterion of a positive definite matrix(239)
Exercise 7.2(241)
7.3 Criterion of Congruent Matrices(242)
Exercise 7.3(245)

Answers to Exercises(246)

Appendix Index(266)

前言/序言

The authors are pleased to see the text of Linear Algebra in English version for Chinese students at the university level. This book not only shows and explains the useful and beautiful knowledge of mathematics, but also presents the structure and arrangement of linear algebra.
1. The Significance of this Book
“One sows a seed in the spring, thousands of grains autumn to him brings.” All the Chinese students had strict training step by step in the study of mathematics before they become a university student. Intuitive and experimental methods are basic and important study patterns, but the target of mathematical education is to form and improve the deductive ability. So far, Chinese students have distinct and excellent achievement in international comparison of mathematics all over the world. As the improvement in educational exchange internationally, more and more Chinese students choose to study abroad at their university level or higher level. Therefore, mathematical textbook on the basis of Chinese students’ mathematical study in English version is urgent needed and essential. This book provides the strong support for the students who will study Economics, Finance, Management, Social Science and so on in local country or abroad.
2. The Difference between Linear Algebra and Calculus
Calculus is mostly about symmetric and beautiful things.One is differentiation, another is its inverse—integration. Calculus can help us to solve the problems in continuous and analog situation in our life. How about other discrete and digital things? Linear algebra can give us help, and vector and matrix are the second type of language we need to study and understand. Study to read a matrix is the most meaningful and key goal in linear algebra, and it gives wide variety for this mathematical area. There are three examples given here:Triangular Matrix,Symmetric Matrix,Orthogonal Matrix.
3. The Structure of this Book
This book organizes the content basis on the logical relationship among number, matrix and vector. It lists the structure from determinant, to matrix, to solve system of linear equations, to vector, to structure of solutions, to eigenvalue and eigenvector, to quadratic form finally.
Here is the structure of this book:
Chapter 1 starts with determinant. There are three important points about the determinant. The first is the definition, the second is property, and the last is its expansion. The Cramer’s rule is given basis on these three points.
Chapter 2 gives all the varieties of matrix. After the study of concept of matrix, it begins with algebra operations, and shows some special matrices. It is following with how to partition matrix, and how to find the inverse of matrix. After given the elementary operations and elementary matrix, this chapter is ended by rank of matrix.
Chapter 3 shows the relationship between matrix and the system of linear equations. Certainly, it is the most important that using matrix to solve the system of linear equations. Gaussian Elimination Method is the most helpful technique.
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