MM848: Matrix manifolds and applications

The Study Board for Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310022102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master

STADS ID (UVA): N310022101
ECTS value: 5

Date of Approval: 13-10-2025


Duration: 1 semester

Version: Approved - active

Internal Course Code

MM848

Comment

This course also exists as part of MM846: Riemannian geometry, matrix manifolds and applications (10 ECTS)

Entry requirements

The course cannot be chosen if you have passed, registered, or have followed MM846 or MM847, or if MM846 or MM847 is a constituent part of your Curriculum.

Academic preconditions

Students taking the course are expected to:

  • Have knowledge of the contents of MM536
  • Have knowledge of the contents of MM540, MM505 or MM568
  • Have knowledge of the contents of MM533
  • Knowledge of MM512 or MM846 is recommended
The course builds on the knowledge acquired in the Bachelor program.The course has connections to MM512: Curves and Surfaces.

Course introduction

The aim of the course is to obtain knowledge of differential geometry and special applications that involve matrix manifolds. The student is enabled: 
  • to analyse, apply and modify these techniques by means of mathematical and numerical analysis 
  • to formulate the problems (including proofs) in a correct mathematical language
  • to make use of these techniques in practical applications

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:
  • understand the basic principles of differential geometry
  • understand and work with matrix manifolds, tangent spaces and curvature
  • compare and contrast the methods introduced in the course
  • transfer the learning content to new problems and applications

Content

The following main topics are contained in the course:
  • Differential submanifolds
  • Tangent spaces
  • Geodesics 
  • The Stiefel and the Grassmann manifolds
  • Optimization and interpolation in matrix manifolds

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Autumn

Tests

Mandatory assignments and oral examination

EKA

N310022102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

All aids allowed

ECTS value

5

Indicative number of lessons

42 hours per semester

Teaching Method

Planned lessons:
Total number of planned lessons: 42
Hereof:
Common lessons in classroom/auditorium: 28
Team lessons in classroom/auditorium: 14

In the lectures, concepts, theories and models are introduced and put into perspective. In the tutorial sessions, the students train their skills through exercises and dig deeper into the subject matter.

Other planned teaching activities:
  • Reading of suggested literature
  • Preparation of exercises in study groups
  • Contributing to online learning activities related to the course

Teacher responsible

Name E-mail Department
Ralf Zimmermann zimmermann@imada.sdu.dk Computational Science

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.