《Linear Algebra A》Syllabus

Course Number:           2109030903 

Course Name:               Linear Algebra A

Instructors:                    Hu Shuangnian

Required Text:       Zhu Yuqing. Linear algebra[M]. Beijing: Science Press, 2021.

Course Description:      This course is a compulsory course, this course can supplement the study of other professional disciplines, cultivate students' logical thinking ability and scientific practice ability, and contribute to the realization of professional training goals. This course mainly teaches the basic knowledge and basic theories of determinants, matrices, linear equations, similar matrices, and quadratic forms, so that students can acquire proficient matrix operation ability and the ability to solve some practical problems with matrix methods, so as to lay the necessary mathematical foundation for learning subsequent courses and further expanding mathematical knowledge. Through the study of this course, students are required to master the basic mathematical theoretical knowledge and thinking methods, gradually cultivate students' ability to analyze and solve problems using mathematical tools in combination with various professional knowledge, and cultivate students' good mathematical cultural literacy, which plays a vital role in students' academic improvement and lifelong learning.

Course Description: 

                                                                                                   Credits/Teaching Hours

Outline of UG CPC Topics Covered in this Course:   (2 Credits/32 Teaching Hours)

Chapter 1 Determinant                                    6 Teaching Hours

Section 1 The Concept of Determinant

Section 2 The Nature of Determinants

Section 3 Determinant Descending Expansion

Section 4 Kramer's Law                                                                       

Chapter 2 Matrix                                         8 Teaching Hours

Section 1: The Concept and Operation of Matrices

Section 2 Inverse Matrices

Section 3 Matrix Partitioning Method

Section 4 Elementary Transformation of Matrices

Section 5 Rank of the Matrix

Chapter 3 Systems of Linear Equations                       8 Teaching Hours

Section 1 Systems of linear equations have conditions for solution

Section 2 Vector groups and their linear combinations

Section 3 Linear Correlation of Vector Groups

Section 4 Rank of Vector Group

Section 5 Structure of a System of Linear Equations Solution                          

Chapter 4 Similarity Matrix                                        10 Teaching Hours

Section 1 The inner product, length and orthogonality of vectors

Section 2 Eigenvalues and eigenvectors of the square

Section 3 Similarity matrices and conditions under which matrices can be diagonalized

Section 4 Diagonalization of Real Symmetry Matrices                                    

Total (Teaching Hours)                                              32  

Summary of UG CPC Topics Covered in this Course:            (32Teaching Hours)