Linear Algebra I

In this lecture we introduce the basic concepts about vector spaces, linear maps and matrix transformations. It is a very important basic course because In many occasions one approaches a problem by linearization, because linear systems are easier to solve than non-linear ones. The syllabus can be found here.

Content: (Organized by chapters in the lecture notes)

1. Linear systems 
2. determinants
3. Euclidean vector spaces 
4. General vector spaces
5. Eigenvalues and eigenvectors
6. Inner product space
7. Diagonalization and quadratic forms
8. Linear transforamations

Literature: 

Final Review problems for the final 

When: Wednesday 24th of January 2024, 08:00-10:00 in then morning. 

Please arrive half an hour before. 

Where: Teaching center, Room 203 

TAs Li Chenxuan, Yu Sun, Zhe Zhelin

Lecture notes

Chapter1 Chapter2 Chapter3 Chapter4 

Chapter5 Diagonalizing Chapter6 Chapter7 Chapter8

Problem sheets 

Sheet1Sheet2 Sheet3 Sheet4 Sheet5 Sheet6 Sheet7 Sheet8 Sheet9 Sheet10.

Sheet11 Sheet12 Sheet13 Sheet14

Midterm review_problems solutions; midterm-solutions.    

Additional material

Proof of Theorem 25 (uniqueness of reduced row echelon form of a matrix)

Applications for Chapter 2 (Cramer's rule and sign of a permutation)

Application-Ch5-Linear-Differential-Equations

Application-Ch5-Spectral-Norm

Proof of Thm235 in Ch5

Applications-Ch7 Conics and local extrema