Course syllabus for Matrix analysis with applications, advanced level

Course syllabus adopted 2024-02-02 by Head of Programme (or corresponding).

Overview

  • Swedish nameMatrisanalys med tillämpningar, avancerad nivå
  • CodeSSY205
  • Credits7.5 Credits
  • OwnerMPICT
  • Education cycleSecond-cycle
  • Main field of studyElectrical Engineering
  • DepartmentELECTRICAL ENGINEERING
  • GradingUG - Pass, Fail

Course round 1

  • Teaching language English
  • Application code 13115
  • Open for exchange studentsYes

Credit distribution

0108 Project 7.5 c
Grading: UG		 7.5 c

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Mathematical analysis and linear algebra.

Aim

Matrix analysis plays a key role in many engineering diciplines both concerning design tools and algorithm as well as for performance analysis. This course will provide a working knowledge of linear algebra and matrix analysis from a user's point of view. Applications in subspace-based methods for signal processing, multivariate statistics and linear systems are considered.

Learning outcomes (after completion of the course the student should be able to)

- solve linear equations
- describe rank, nullspace and range space of a matrix
- describe, solve and analyse multivariable least-squares problems
- use Kronecker products to reformulate and analyse matrix equations
- describe eigenvalues, similarity transforms and quadratic forms
- describe singular value decomposition and use it for analysis
- use matrix culculus to perform analysis

Content

Matrices and Gaussian elimination, Vector spaces and linear equations,
Orthogonality and projections, determinants, diagonalization, eigenvalues and eigenvectors, singular value decomposition. subspace-based methods, quadratic-forms, Kronecker products, matrix calculus, Lyapunov equations and sample covariance statistics. Examples from signal processing and estimation.

Organisation

Lectures, Tutorials and Home assignments

Literature

See course homepage

Examination including compulsory elements

Written examination

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.