In this course, we will cover the following contents: Systems of linear equations, Gaussian elimination, matrices, determinants, and Cramer’s rule. Vectors, vector spaces, basis and dimension, linear transformations. Eigenvalues, eigenvectors, and quadratic forms.Objective:Solve and Interpret systems of linear equations.Understand the elementary facts of abstract vector space.Understand the linear transform
三🤱、教学内容、教学方式和学时安排
课堂教学内容
教学进度和学时安排
教学方式
Systems of Linear Equations and Matrices
1.1 How to solve a system of Linear equations by Gaussian elimination ?
1.2 Matrix and its main properties.
1.3 Elementary matrices and invertible matrices.
10学时
线上教学、
课后复习（作业）、
讨论和拓展
Determinants
2.1 Definition of determinants.
2.2 Evaluating determinants.
2.3 Properties of determinants and Cramer’s rule.
6学时
线上教学、
课后复习（作业）、
讨论和拓展
Euclidean Vector Spaces
3.1 Introduction to n-space.
3.2 Norm, dot product in R^n and its geometry.
3.3 Orthogonality and a new insight of linear system by geometry.
3.4 Cross product.
6学时
线上教学、
课后复习（作业）👩🏿🏫、
讨论和拓展
4 General Vector Spaces
4.1 Vector spaces and subspaces.
4.2 Linear independence.
4.3 Basis and dimension.
4.4 Change of basis.
4.5 Fundamental spaces and rank, nullity of a matrix.
4.6 Matrix transformations.
4.7 Geometry of matrix operators.
16学时
线上教学、
课后复习（作业）💅、
讨论和拓展
Midterm exam （待定）
2学时
闭卷
Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors.
5.2 Diagonalization
5.3 Complex vector spaces.
6学时
课堂教学⚒、
课后复习（作业）🧜🏿♀️、
讨论和拓展
6 . Inner Product Spaces
6.1 Inner product and orthogonality in inner product space.
6.2 Gram-Schmidt process.
6.3 Best approximation and least squares.
5学时
课堂教学、
课后复习（作业）、
讨论和拓展
7. Diagonalization and Quadratic Forms
7.1 Orthogonal matrices.
7.2 Orthogonal diagonalization.
7.3 Quadratic forms.
5学时
课堂教学、
课后复习（作业）🔬、
讨论和拓展
8. Linear Transformations
8.1 General linear transformations and isomorphism.