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课程

中国大学MOOC,为你提供一流的大学教育

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Linear Algebra
第6次开课
开课时间: 2025年03月18日 ~ 2025年07月28日
学时安排: 3-5小时每周
进行至第8周,共19周 已有 6 人参加
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课程详情
课程评价(101)
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课程概述

This course "Linear Algebra with Applications" covers a comprehensive and systematic basic theory of linear algebra, and some practical applications in our social life and scientific research nowadays.We use foreign classic textbooks, with a complete and clear PPT. The teacher has more than ten years of teaching experience of this course using English, and the members/assistant of our team also have rich teaching experience. By learning our course, you will understand the beauty of linear algebra, grasp rich knowledge points, lay a good foundation for subsequent courses; By learning our course, you will know that linear algebra has a wide range of fresh applications, rather than boring concepts, theorems and formulas; By learning our course, you will learn the English expression of linear algebra knowledge, be familiar with the scientific and technological English writing, which help you to be integrated your academic study and scientific research with the world. Welcome to join our course "Linear Algebra with Applications" of Beijing Jiaotong University! Enjoy the beauty of Linear Algebra!

授课目标

The course "Linear Algebra with Applications" mainly teaches the basic concepts and theorems of linear algebra. Taking Gauss elimination method for solving linear equations and solving linear equations as the breakthrough point and main line, a series of knowledge points such as matrix, determinant, vector space, orthogonality and eigenvalue, eigenvector and positive definite matrix are introduced. It focuses on the combination of basic knowledge and theory with practical application, including the application of linear algebra knowledge in web search, population migration, economic model, computer image transformation, least squares problem, spatial analytic geometry, etc. This course not only contains the basic theory of classical linear algebra, but is also close to some practical applications that we pay attention to at present.

课程大纲
Matrices and Systems of Equations
1.1 Systems of Linear Equations
1.2 Row Echelon Form
1.3 Matrix Algebra
1.4 Elementary matrices
1.5 Partitioned Matrices
Determinants
2.1 Determinant
2.2 Properties of Determinant
2.3 Additional Topics and Applications
Vector Spaces
3.1 Definition and Examples
3.2 Subspaces
3.3 Linear Independence
3.4 Basis and Dimension
3.5 Change of Basis
3.6 Row Space and Column Space
Linear Transformations
4.1 Definition and Examples
4.2 Matrix Representation of Linear Transformations
4.3 Similarity
Orthogonality
5.1 The Scalar Product in Rn
5.2 Orthogonal Subspaces
5.3 Least Squares Problems
5.4 The Gram-Schimidt Orthogonalization Process
Eigenvalues
6.1 Eigenvalues and Eigenvectors
6.2 Diagonalization
6.3 Quadratic Forms
6.4 Positive Definite Matrices
展开全部
Beijing Jiaotong University
1 位授课老师
Chao ZHANG

Chao ZHANG

Professor

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