Linear algebra is a public basic course for many majors such as science, engineering, economics and management, and it provides essential mathematical tools for various fields of modern society. Linear algebra is a course that discusses the classic theory of linear relationships in finite dimensional spaces. It has strong abstraction and logic, and is an important basic theory course for undergraduates of science and engineering universities. This course is not only a mathematical foundation that students must master, but also has a very wide range of applications in various fields of modern science and technology.

With the rapid development of big data, cloud computing, Internet of Things, artificial intelligence and other information technologies, modern society is entering the data era in an all-round way. Matrix algebra is the basic language of the data era and has been widely used in various fields of modern science and technology. Many practical problems can be discretized and linearized, and thus transformed into linear algebra problems. For example, the design of network search engines, aircraft design, big data processing, computer image processing, 3D animation, virtual reality, etc., everywhere reflect the perfect fusion of algebra, geometry and the real world.

This course includes six parts: determinant, matrix, linear correlation of vector groups, linear equation system, similar transformation of matrix, quadratic form.

Through the study of this course, the following teaching objectives should be achieved:

1. In view of the fact that this course is relatively abstract for beginners, it introduces relevant concepts and deepens the understanding of relevant theorems through more practical examples and intuitive geometric figures, combined with spatial analytical geometry.

2. Through the proof and application of relevant theorems, gradually cultivate students' abstract thinking ability and rigorous reasoning ability, as well as the ability to use linear algebra to analyze basic problems.

3. To enable students to master the basic theories and research methods of linear algebra, and to use them more flexibly.

4. Cultivate students' ability of abstract thinking and logical thinking, use the basic theory of linear algebra to analyze problems, and lay a good foundation for students to further study other mathematical courses and professional courses.

High school math algebra related knowledge

"Linear Algebra", published by Beijing University of Aeronautics and Astronautics

Author: Gao Zongsheng, Zhou Meng, Li Hongyi

"Linear Algebra", Higher Education Press

Author: Li Shangzhi