Linear Algebra (Third Edition)

Name: Linear Algebra (Third Edition)
ISBN: 9787562854937

刘剑平 / 鲍亮 / 施劲松 / 钱夕元 / 朱坤平East China University of Science and Technology Press · ChinaJan 2021

3.5

Word count: 105K words
Chapters: 80
ISBN: 9787562854937

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Summary

This book was written in accordance with the "Basic Requirements for the Teaching of Linear Algebra Courses" revised in 1995 by the Steering Committee for Mathematics Courses in Higher Engineering Education, and draws on the author's many years of teaching experience. It covers the basic content of linear algebra courses for non-mathematics majors in higher education: matrices, determinants, the rank of a matrix and systems of linear equations, vector spaces, eigenvalue problems, quadratic forms, linear spaces and linear transformations, and more, meeting the requirements of the syllabus for the master's entrance examination for non-mathematics candidates. The book can be used as a textbook for undergraduates in engineering departments and in non-mathematics science departments at colleges and universities, and can also be read and consulted by scientists and engineers.

Editor's review

Professor Liu Jianping's Linear Algebra (Third Edition) is a classic foundational textbook for science and engineering students published by East China University of Science and Technology Press, recognized by many university faculty and students for its clear structure and pragmatic style. Its most prominent feature is the balance between theory and application—it systematically explains core concepts of linear algebra such as matrices, determinants, vector spaces, linear transformations, and eigenvalues, while also helping students build intuitive understanding through numerous examples and exercises drawn from engineering, economics, and other fields, avoiding the maze of pure abstraction. Compared with some textbooks that pursue mathematical rigor at the cost of being somewhat obscure, this book is written in a plainer style with detailed step-by-step breakdowns, making it very suitable as a first guide for beginners building a knowledge framework.

The third edition has been optimized on the basis of earlier versions: the order of some chapters has been adjusted so that the knowledge thread better follows the patterns of cognition; exercises have been updated and supplemented; and preliminary guidance on combining the material with computer computation (such as MATLAB) has been added, reflecting trends in the discipline. For self-learners, another advantage of this book is its patient explanations—key theorems and formulas are usually accompanied by geometric interpretations or descriptions of application scenarios, lowering the barrier to self-study. Overall, this is a solid, reliable textbook oriented toward teaching effectiveness; its value lies not in proposing startling new theories but in steadily and clearly fulfilling the core task of imparting basic knowledge and basic skills.

Who it's for

A good fit for

Lower-division undergraduates in science and engineering majors (such as engineering, physics, and computer science), using it as a course textbook or companion reference
Students preparing for graduate entrance examinations who need to review or consolidate foundational knowledge of linear algebra
Working professionals in engineering and technical fields who need to revisit or apply linear algebra tools
Self-learners who prefer textbooks with a step-by-step approach, detailed explanations, and abundant examples

Not a good fit for

Upper-division mathematics students or researchers who seek depth of mathematical theory and formal rigor and wish to explore abstract algebraic structures in depth
Readers without a science or engineering background who only need to understand the most central ideas of linear algebra and want a quick overview

Reading tips

Study the chapters in order, paying special attention to the exercises at the end of each chapter—this is the key to turning concepts into problem-solving ability
Keep scratch paper at hand while reading and personally derive the important theorems and example calculations in the book to deepen your impression
Think of matrix operations in connection with intuitive images of geometric space transformations; this can greatly enhance your understanding of the essence of linear algebra

About the publisher

East China University of Science and Technology Press China · Founded in 1986

East China University of Science and Technology Press is a comprehensive university press known for publishing university textbooks, academic monographs and supplementary teaching materials, and it has also developed a distinctive list in classics and foreign literature. Its 825 titles in the library cover common categories such as classics, foreign literature, inspirational growth and social novels. Representative books include the Japanese editions of Selected Works of Lu Xun (The True Story of Ah Q, Hometown, Medicine, Kong Yiji and A Madman's Diary), the English original edition of Agatha Christie's And Then There Were None, the English edition of Antoine de Saint-Exupéry's The Little Prince, and English and American literary readers such as Anne of Green Gables. Its authors range from Lu Xun and Inoue Kōbai in Chinese and Japanese literature to foreign writers such as Christie, Montgomery and Fitzgerald, as well as Zhu Wei and Xu Naifu. Overall, the press balances textbooks and academic works with general reading, giving equal weight to Chinese and foreign literary classics.

版权信息
本书编委会
前言
1 矩阵
1.1 矩阵的概念
1.2 矩阵的运算
1.3 逆矩阵
1.4 矩阵的分块
1.5 初等变换与初等矩阵
1.6 应用举例
1.7 Matlab辅助计算
习题一
2 行列式
2.1 行列式的定义
2.2 n阶行列式的展开公式
2.3 行列式的性质
2.4 行列式的计算
2.5 行列式的应用
2.6 应用举例
2.7 Matlab辅助计算
习题二
3 矩阵的秩与线性方程组
3.1 矩阵的秩
3.2 齐次线性方程组
3.3 非齐次线性方程组
3.4 应用举例
3.5 Matlab辅助计算
习题三
4 向量空间
4.1 向量组的线性相关与线性无关
4.2 向量组的秩
4.3 向量空间
4.4 线性方程组解的结构
4.5 向量的内积
4.6 应用举例
4.7 Matlab辅助计算
习题四
5 特征值问题
5.1 方阵的特征值与特征向量
5.2 相似矩阵
5.3 实对称矩阵的对角化
5.4** 约当标准形
5.5 应用举例
5.6 Matlab辅助计算
习题五
6 二次型
6.1 二次型及其标准形
6.2 正定二次型与正定矩阵
6.3 应用举例
6.4 Matlab辅助计算
习题六
7 线性空间与线性变换**
7.1 线性空间的定义与简单性质
7.2 基、维与坐标
7.3 基变换与坐标变换
7.4 线性变换
7.5 线性变换的矩阵表示
7.6 应用举例
7.7 Matlab辅助计算
习题七
习题答案
附录1 Matlab软件简介
1 Matlab概述
2 数组（向量）
3 矩阵
4 常量、变量、函数
5 绘图函数
6 符号运算
7 命令环境与数据显示
8 程序设计
附录2 线性代数期终试卷
试卷一
试卷二
试卷三
试卷四
试卷五
试卷六
试卷答案及提示
参考文献
内容提要

FAQ

How does this book differ from Tongji University's Linear Algebra?

This book places greater emphasis on a step-by-step approach and detailed explanation, and its examples and exercises have richer application contexts, which may be friendlier to beginners. The Tongji edition is more concise, is used more widely across the country, and has a relatively classic style. Both are excellent textbooks; choose according to your personal study habits and course requirements.

Does this book include content on numerical computation or computer applications?

The third edition introduces some preliminary material and discussion questions related to computer computation, such as mentions of MATLAB software. But it is not a dedicated textbook on numerical linear algebra; its main focus remains the classic theories and methods of linear algebra.

What mathematical background is required to use this book for self-study?

A high school mathematics foundation is required, especially basic knowledge of vectors and systems of equations. The book introduces the subject starting from these foundational concepts, so with that background you can follow it for self-study.

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About the author

刘剑平 Author

Liu Jianping is an author known in the Chinese book market for mathematics study guides. Public information about him is limited, and his nationality, dates of birth and death, and academic background are not clearly recorded. Three of his works are included in the collection: Synchronized Tutoring and Complete Solutions to Exercises for Linear Algebra, Synchronized Tutoring and Complete Solutions to Exercises for Calculus (Higher Education Press, Wu Chuansheng, 3rd Edition), and Linear Algebra (Third Edition). These titles show that his writing focuses on foundational science and engineering courses such as advanced mathematics and linear algebra, usually presented as synchronized tutoring, complete exercise solutions, and textbook companions for university students' study and review. Such books closely follow the chapters of mainstream textbooks and emphasize clear solution steps and standard methods, appearing in the science popularization and examination categories and suited to both classroom use and systematic pre-exam practice.

鲍亮 Author

Bao Liang: publicly available information is limited, and a complete biography, educational background, and professional experience cannot currently be confirmed. Within the library's holdings, the author is associated with Linear Algebra (Third Edition), a work classified under exam preparation, indicating that its content mainly serves course study and test review needs. As a foundational course for science, engineering, and economics and management students, linear algebra emphasizes the connection between conceptual understanding and problem-solving practice. Textbooks of this kind typically focus on precise definitions, the derivation of theorems, and graded exercises, helping readers build a clear knowledge framework for review and examinations. Because verifiable information is scarce, this introduction is based only on the subject matter and category of the work, without speculation about the author's personal history; the author's writing style and specific influence await further material.

施劲松 Author

Information about Shi Jinsong is rather limited in publicly available sources. What can be confirmed is that he is the author of the textbook Linear Algebra (Third Edition), a work classified in book listings under examination preparation. Based on the available information, his writing centers on linear algebra, a foundational mathematics course, and is aimed at readers who need systematic review and exam-oriented practice. Linear algebra covers core topics such as vectors, matrices, systems of linear equations, and spaces, and textbooks in this area typically emphasize precise conceptual statements, worked examples, and graded exercises. As the author of a third edition, his work would presumably involve refining the structure, correcting errors, and making the presentation better suited to teaching and exam preparation. In the absence of biographical details, readers' understanding of the author comes mainly from this textbook itself; its style and influence should likewise be understood in light of the book's position among exam-preparation titles, namely as a clear and practical aid for learners mastering the basic methods and problem-solving approaches of linear algebra.

钱夕元 Author · Chinese

Qian Xiyuan is a Chinese author about whom relatively limited public information is available. The only confirmed work is Linear Algebra (Third Edition), a book commonly classified under exam preparation and intended for readers whose main goals are exam readiness and course review. The subject belongs to linear algebra, a foundational university mathematics course, and works of this kind typically cover core topics such as matrices, vectors, and systems of linear equations, with attention to precise definitions and the training of problem-solving methods. As the compiler of a textbook or study guide, Qian Xiyuan's role is mainly one of organizing, arranging, and presenting existing teaching content rather than conducting original theoretical research. Since only one work is held in the collection, a full assessment of the author's writing style and academic orientation is difficult; readers should choose the book in light of their own course requirements and exam syllabi, using it as one reference for review and practice.

朱坤平 Author

Zhu Kunping: publicly available information is limited, and details such as nationality, dates of birth and death, and English name cannot currently be confirmed. According to the library's holdings, the work attributed to this author is Linear Algebra (Third Edition), which is classified under exam preparation, indicating that the author's writing relates to teaching support and exam preparation for a foundational mathematics course. As linear algebra is an important basic course for students in science, engineering, economics, and management, related textbooks and study guides typically emphasize concept review, formula derivation, and exercise practice, and Zhu Kunping's work likely serves this learning context as well. Since no other works or biographical details by this author appear in the library records, a full assessment of the author's writing style and academic influence must await further information.