# MATA125 Matrix Analysis (4 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

Real and complex vector spaces; eigenvalues; Hermitian, unitary and normal matrices; definiteness of matrices; matrix decompositions incl. spectral and singular value decomposition; matrix norms.

## Learning outcomes

After completing the course the student

- understands the connection between linear mappings and matrices
- knows complex vector spaces and knows how to use the complex inner product in examining matrices
- knows different types of matrices and their properties
- is able to solve whether a square matrix is diagonalizable and determine its spectral presentation
- is able to determine the definiteness of a square matrix and compute its square root
- knows how to compute certain matrix decompositions and knows some of their applications
- knows how to compute different matrix norms and knows some of their applications

## Description of prerequisites

Linear algebra and geometry 1 and 2, basics on complex numbers

## Study materials

Luentomoniste

## Literature

- Stephen Barnett, Matrices: Methods and Applications
- Mikko Saarimäki, Matriisiteoria (luentomoniste)
- Fuzhen Zhang, Matrix Theory

## Completion methods

### Method 1

**Evaluation criteria:**

Arvosana määräytyy kurssitentin pistemäärän ja laskuharjoitushyvitysten perusteella.

Select all marked parts

### Method 2

**Evaluation criteria:**

Final exam.

Select all marked parts

**Parts of the completion methods**

x

### Teaching (4 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Language:**

Finnish

**Study methods:**

Lectures 28h (in Finnish) and homework

#### Teaching

##### 10/23–12/17/2023 Lectures

##### 12/14–12/14/2023 Exam

##### 1/17–1/17/2024 Exam

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Language:**

English, Finnish

**Study methods:**

Independent study and final exam.