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)

- Linear systems
- determinants
- Euclidean vector spaces
- General vector spaces
- Eigenvalues and eigenvectors
- Inner product space
- Diagonalization and quadratic forms
- Linear transforamations

**Literature: **

Book Name: Elementary Linear Algebra (Application Version),

Howard Anton & Chris Rorres, ISBN 978-1-118-43441-3, Wiley, 2014, Edition 11

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.