Linear algebra

Author: Hu Shurong, Zhang Jing, Li Xiucheng (editors)
Publisher:
Publishing Date: 2006-08-01
Features: Since the 21st century, China's higher education has made remarkable progress, and textbook development has also advanced significantly. Currently, science and technology are evolving rapidly, with the widespread application of computers and the popularity of mathematical software, the world has fully entered the information age. These developments undoubtedly impose new and stricter requirements on foundational textbooks, especially those for mathematics courses. In this context, based on summarizing years of undergraduate mathematics teaching experience, exploring the development trends of undergraduate mathematics education, and analyzing the trends of similar textbooks domestically and internationally, we have compiled this linear algebra textbook suitable for students of all majors at the undergraduate level. This book is written in accordance with the "Basic Requirements for Linear Algebra Course Teaching" formulated by the Ministry of Education. It adheres to the principles of emphasizing the cultivation of fundamental concepts and abilities while striving to align closely with practical applications, and it fully considers the trend of reduced teaching hours for linear algebra courses. The book has the following features:
First, it highlights the fundamental ideas and methods of linear algebra. The purpose of emphasizing these is to help students better understand the internal connections among different parts of the content during their learning process, enabling them to grasp the overall ideas and methods of linear algebra. It also assists students in mastering fundamental concepts, clarifying the relationships between them, and improving teaching effectiveness. In terms of teaching philosophy, it does not overly emphasize rigorous proofs or research processes but instead focuses more on allowing students to appreciate the essence and value of linear algebra.
Second, it strengthens the cultivation of fundamental abilities. The book includes numerous examples and exercises, with in-depth discussions on problem-solving methods. The intention is to help students, after grasping the basic concepts, become familiar with computational processes, master problem-solving techniques, and ultimately achieve faster calculation speeds and enhanced problem-solving skills.
Third, it is closely aligned with practical applications. The book strives to introduce fundamental concepts from real-world problems encountered in daily life. Examples and exercises often involve practical issues frequently faced in the objective world, such as those in natural sciences, engineering technology, economic management, and daily life. The hope is to enhance students' interest in learning linear algebra and their ability to apply linear algebra knowledge to solve real-world problems. Considering the varying needs of different disciplines, some chapters are marked with an asterisk "" for selection by relevant majors.
The book consists of 7 chapters, covering topics such as determinants, matrices and their operations, elementary transformations of matrices and systems of linear equations, the linear dependence of vector sets, eigenvalues and eigenvectors of matrices, quadratic forms and their standard forms, linear spaces and linear transformations. Each chapter is accompanied by exercises, and the answers to the exercises are provided at the end of the book.