MATA125 Matrix Analysis (4 cr)

Open the course unit brochure on Sisu
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

x

Exam (4 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish
Study methods:

Independent study and final exam.

Teaching