Linear Algebra
Undergraduate course, Guangdong University of Petrochemical Technology, Computer Department, 2025
Linear algebra is a basic lesson of the advanced mathematics in college education. Also, it provides the fundamental calculating rule to the engineering and information science disciplines.
Moreover, linear algebra plays significate role in most technology and sciences because of calculating efficiently and constructing natural patton to model. Even if the nonlinear models, which is difficultly developed into linear model, there are the differential of a multivariate ways at a fixed area mapped into the best approximate field of the linear functions. Two reference books for learning linear algebra, linear algebra textbook and linear algebra lesson.
Answers to textbook exercises: Chapter 1, Chapter 2, Chapter 3, Chapter 4.
| Chapter | Date/Slides | Tasks | Description |
|---|---|---|---|
| Ch1 Determinant | 0930 | none | order 2 and 3 determinant |
| 1010 | none | order n determinant | |
| 1010 | none | properties of determinant | |
| 1014 | Exercise1 | determinant expansion | |
| 1017 | Answer1,homework | Cramer formula | |
| Ch2 Matrices | 1021, 1024 | none | Matrix definition and calculation |
| 1024 | Exercise2 | Inverse Matrix | |
| 1028 | Exam | Partitioned matrices | |
| 1031 | Answer2 | Matrix elementary transformation | |
| 1031 | none | Matrices rank | |
| Ch3 Linear System | 1104, 1107 | none | Solutions to a system of linear equations |
| 1111 | homework | sets of vectors and its linear combination | |
| 1118 | none | linearly dependent vectors | |
| 1121 | Exercise3 | rank of a set of vectors | |
| 1125 | none | structure of solutions to linear systems | |
| 1125 | Answer3, homework | vector space | |
| Ch4 Normal matrix | 1128 | Exercise4 | dot product |
| 1202 | Answer4 | Eigenvalue, eigenvector | |
| 1205 | Exercise5 | similar matrix | |
| 1209 | Answer5 | diagonalization | |
| 1212 | none | quadratic form, standard form | |
| 1216 | none | positive-define matrix | |
| 1219 | LM cheat sheet | Review |