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.
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 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 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
Chapter 6 Quadratic test