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: 

Lectures: Wednesdays and Fridays 8:15-9:55 Teaching building Room 303.

Example classes 

Wednesdays 18:00-19:40  SPST 1-205 (Li Chenxuan) 

Fridays 18:00-19:40 SPST 1-105 (Yu Sun)

Fridays 16:00-17:40 SIST 1A108 (Zhe Zhelin)

Every student is attached to one example class. 

I strongly recommend to attend the example classes.

The lecture notes will be published here: Chapter1 Chapter2 Chapter3

Chapter 4: Week8 Week9 Week10-1 Week10-2(end of Chapter4)

Chapter 5: Week10-2(Beginning of Chapter 5) 

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)

The problem sheets are published weekly, and the solution has to be handed in by Wednesday before the lecture.  

Sheet1Sheet2 Sheet3 Sheet4 Sheet5 Sheet6 Sheet7 Sheet8

For the midterm we provide a collection of review problems for self-study: 

The midterm covers Chapter1 to Chapter 4. 

review_problems