课堂教学内容

教学进度和学时安排

教学方式

1. 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

2.  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

3. 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

5. 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.

8.2 Compositions and inverse transformations.

8.3 Matrices for general linear transformations.

8.4 Similarity.

6学时

课堂教学、

课后复习（作业）、

讨论和拓展

期末考试

2学时

闭卷