Linear Algebra

Name: Linear Algebra
ISBN: 9787301105818

卢刚Peking University Press · ChinaAug 2025

3.4

Word count: 96K words
Chapters: 41
ISBN: 9787301105818

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Summary

This book is a textbook for the "Linear Algebra" public course for undergraduate students in economics and management at colleges and universities.

Editor's review

This is a linear algebra textbook for undergraduates in economics and management at colleges and universities, organized to fit classroom hours and the needs of subsequent courses in the field. Its value lies in clearly explaining basic tools such as matrices, vectors, and systems of linear equations, and in helping readers understand their foundational role in economics and management. The textbook typically includes worked examples and exercises, and is suitable for step-by-step chapter learning. Readers should not merely memorize formulas but focus on how concepts connect: from systems of equations to matrices, from matrix operations to vector spaces, forming a reusable problem-solving approach. For readers in economics and management, mastering the book's basic methods matters more than pursuing abstract proofs; working through the exercises alongside the course schedule and checking understanding promptly is recommended.

Who it's for

A good fit for

Undergraduates in economics and management taking the linear algebra public course
Upper-year economics and management students who need to make up foundational linear algebra
Readers preparing for graduate entrance exams in economics and management who need to review basic concepts and operations

Not a good fit for

Mathematics majors seeking more abstract and advanced theoretical proof training
Researchers who have already systematically studied linear algebra and only want to consult frontier applications

Reading tips

Study in chapter order; read the worked examples in each section first, then complete the end-of-chapter exercises independently.
Keep an error notebook recording common mistakes in matrix operations and solving systems of equations.
After finishing each chapter, use a mind map to organize conceptual relationships and avoid memorizing formulas in isolation.

About the publisher

Peking University Press China · Founded in 1979

Peking University Press is a comprehensive university press whose publishing areas cover classical literature, popular science, social culture, world history, Western philosophy, and culture. Its catalogue contains 6,031 titles, with representative books including A Dream of Red Mansions, Relativity: The Special and General Theory (15th Edition) (with Einstein's classic papers on unified field theory and other topics), Elements, Conics, The Aristocratic Families of the Eastern Jin, The Philosophy of Mythology (Volume I), The Philosophy of Mythology (Volume II), and The Origin of Continents and Oceans. Representative authors include Cao Xueqin, Zhou Ruchang, Albert Einstein, Euclid, Apollonius, Tian Yuqing, Schelling, and Xian Gang. The press has developed distinctive strengths in classical Chinese literature and in the translation of Western philosophical classics, while also covering scientific classics and social and cultural studies. As public information is limited, this description is based only on the books in the catalogue and offers no further extrapolation.

版权信息
内容简介
《21世纪高等院校经济管理学科数学基础系列教材》编审委员会
前言
第一章行列式
1.1 矩阵的概念
1.2 n阶矩阵的行列式
1.3 行列式的性质
1.4 行列式计算中的几种基本方法
1.5 行列式按k行（列）展开
1.6 克拉默（Cramer）法则
总习题一
第二章矩阵的运算
2.1 矩阵的运算
2.2 矩阵的分块
2.3 可逆矩阵
2.4 矩阵的初等变换
2.5 矩阵的秩
总习题二
第三章线性方程组
3.1 线性方程组的消元解法
3.2 n维向量及其线性运算
3.3 向量间的线性关系
3.4 向量组的秩
3.5 线性方程组解的结构
3.6 Rn的标准正交基
总习题三
第四章矩阵的特征值与特征向量
4.1 矩阵的特征值与特征向量
4.2 相似矩阵与矩阵的对角化
4.3 实对称矩阵的特征值与特征向量
4.4 两个应用的例子
总习题四
第五章二次型
5.1 基本概念
5.2 二次型的标准形
5.3 惯性定理与二次型的规范形
5.4 正定二次型与正定矩阵
总习题五
习题参考答案与提示
参考书目

FAQ

Is this book suitable for self-studying linear algebra?

It can serve as self-study material, but readers need basic algebraic computation skills. Proceed chapter by chapter: understand definitions and examples first, then do the exercises. For proof-oriented content, grasp the conclusions and their use first; there is no need to pursue fully independent derivation from the start. Results are more reliable when combined with a class or online course.

Where should economics and management students focus when studying this book?

Focus on basic tools such as matrix operations, solving systems of linear equations, and linear dependence of vector sets, and understand how they are used in economics and management problems. For overly abstract proofs, go as far as your capacity allows; first ensure concepts are clear and calculations accurate, then gradually deepen understanding.

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About the author

卢刚 Author

Public information about Lu Gang is limited: all that is known is a single work, Linear Algebra, classified on this site under exam preparation. This suggests that the author's writing focuses on foundational mathematics courses and study or test-preparation support, aimed at students who need to review linear algebra systematically and prepare for related examinations. Linear algebra is a core course for science, engineering, and economics and management students; its content is abstract and dense with symbols and derivations, making it demanding for beginners. Books of this kind typically need to balance conceptual explanation, worked examples, and exercise practice, helping readers connect definitions, theorems, and computational steps into usable problem-solving routines. Because no biographical, educational, or professional details are available, the author's teaching background cannot be confirmed, nor should the specific features of the writing style be inferred. The work can only be judged as serving the practical needs of course study and exam preparation, suitable as supplementary review material.