请点击右上角按钮，选择“在Safari中打开”
再点击页面中的下载或打开
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.
Chapter 1 Determinant
1.1 Definition of n-order determinant
1.2 The property of the determinant
1.3 Expansion and calculation of determinant
1.4 Cramer's rule
Chapter 1 Determinant Test
Chapter 2 Matrix
2.1 The concept of matrix
2.2 Matrix operation
2.3 Inverse matrix
2.4 block matrix
2.5 Elementary transformation and elementary matrix
2.6 The rank of the matrix
Chapter 2 Matrix Test
Chapter 3 Linear correlation of vector groups
3.1 The concept and operation of vector
3.2 Linear correlation of vector groups
3.3 Rank of vector group
3.4 Vector Space
Chapter 3 Linear correlation of vector groups Test
Chapter 4 Linear equations
4.0 The introduction of the problem
4.1 The decision theorem for the solution of linear equations
4.2 The solution of linear equations
4.3 Structure of the solution of linear equations
Chapter 4 Linear equations Test
Chapter 5 Matrix similarity transformation
5.1 Eigenvalues and Eigenvectors of Square Matrix
5.2 Similar diagonalization of matrices
5.3 Similar diagonalization of real symmetric matrices
Chapter 5 Matrix similarity transformation Test
Chapter 6 Quadratic
6.1 Quadratic form and its matrix representation
6.2 Turn quadratic form into standard form
6.3 The inertia theorem
6.4 Positive definite quadratic form and positive definite matrix
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
professors/doctoral tutors
professors/doctoral tutors
Associate Professor
