# MATA125 Matrix Analysis (4 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

## 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

Luentomoniste

## Literature

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

## Completion methods

### Method 1

Evaluation criteria:
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
0-5
Language:
Finnish
Study methods:

Lectures 28h (in Finnish) and homework

x

Type:
Exam