Linear Algebra and Its Applications

Author: Wang Xiaofeng, Editor-in-Chief
Publisher:
Publish Date: 2002-02-01
Features: Linear algebra theory has a long history and rich content. With the development of science and technology, especially the increasing use of electronic computers, as one of the important mathematical tools, the application of linear algebra has been deeply integrated into various fields such as natural sciences, social sciences, engineering technology, economics, and management. As a result, many departments in universities regard linear algebra as one of the essential foundational courses, which also raises higher requirements for the teaching content and methods of linear algebra. Based on this knowledge, this textbook not only takes into account the comprehensiveness, systematic nature, and logical rigor of linear algebra but also strives to highlight the following distinctive features: It applies the elementary row operations of matrices, one of the most important tools in linear algebra, throughout the book, allowing students to fully appreciate its powerful functionality. The first chapter introduces systems of linear equations, which is simply a continuation of secondary school algebra, enabling students to quickly get into the topic and avoiding the awkwardness of introducing complex and difficult-to-grasp concepts like determinants at the beginning. It reduces the content of determinants, which are not frequently used and hold little significance, and defines determinants using practical row or column expansion methods, minimizing their use in other content (e.g., the definition of matrix rank). It employs formal matrix notation (or views it as a block matrix) to handle linear relationships between vector groups, simplifying complex calculations and related proofs. It provides as many application examples as possible, allowing students from various disciplines to experience the usefulness of linear algebra for their professional development and thereby increasing their interest in learning. It has good flexibility, allowing teachers to select or omit certain content based on the number of teaching hours (e.g., if there are only 30–40 hours, the content marked with “”, part of Chapter 7, and part or all of Chapter 8 can be omitted).