Skip to main content

EQ2820 Matrix Algebra, Accelerated Program 7.5 credits

This is a course aimed at an intermediate undergraduate/graduate level that will be given on a regular basis (depending on interest and resources). We will refresh and extend the basic knowledge in linear algebra from previous courses in the undergraduate program. Matrix algebra is of fundamental importance for scientists and engineers in many disciplines. In this course we will focus on topics that are of particular interest in communications, signal processing and automatic control.

The course requires a large amount of self study and homework problems will be handed out every week and will be due the following week. The course assumes some familiarity with basic concepts from linear algebra (as one can expect from talented final year undergraduates).

About course offering

For course offering

Spring 2022 Start 21/03/2022 programme students

Target group

Open to all programmes

Part of programme

Master's Programme, Information and Network Engineering, åk 1, Recommended

Master's Programme, Information and Network Engineering, åk 1, COE, Recommended

Master's Programme, Information and Network Engineering, åk 1, INF, Recommended

Periods

P4 (7.5 hp)

Duration

21/03/2022

07/06/2022

Pace of study

50%

Form of study

Normal Daytime

Language of instruction

English

Course location

KTH Campus

Number of places

Min: 10

Planned modular schedule

No information inserted

Application

For course offering

Spring 2022 Start 21/03/2022 programme students

Application code

60243

Contact

For course offering

Spring 2022 Start 21/03/2022 programme students

Examiner

No information inserted

Course coordinator

No information inserted

Teachers

No information inserted
Headings with content from the Course syllabus EQ2820 (Spring 2022–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Main contents:

  1. Repetition of vector spaces, inner product, determinant, rank
  2. Eigenvalues, eigenvectors and characteristic polynomials
  3. Unitary equivalence, QR-factorisation
  4. Canonical forms, Jordan form, polynomials and matrices
  5. Hermitian and symmetric matrices, variational characterisation of eigenvalues, simultaneous diagonalisation
  6. Norms for vectors and matrices
  7. Localisation and disturbance of eigenvalues 
  8. Positive definite matrices. Singular value decomposition 
  9. Nonnegative matrices, positive matrices, stochastic matrices
  10. Stable matrices; Liapunov's theorem 
  11. Matrix equations, Kronecker product and Hadamard product 
  12. Matrices and functions, square roots, differentiation

Intended learning outcomes

After passing the course, the student should be able to

  • use and explain some basic tools (be specified by the course content) in matrix algebra
  • identify scientific problems where tools from matrix algebra can be powerful
  • apply the matrix algebra knowledge to solve and analyse the identified problems

For higher grades, the student should also be able to

  • combine several partial problems and solutions to solve and analyse more complex problems.

Course disposition

No information inserted

Literature and preparations

Specific prerequisites

Knowledge in linear algebra, 7.5 higher education credits, equivalent  to completed course SF1624.

Knowledge in mathematical analysis, 15 higher education credits, equivalent to completed courses SF1625 and SF1626.

Recommended prerequisites

Good knowledge of first course in linear algebra. Admission is by request to examiner.

Equipment

No information inserted

Literature

Announced on the course website four weeks before the start of the course.

We have previously used "Matrix Analysis" and "Topics in Matrix Analysis" by R.A. Horn and C. Johnson

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F

Examination

  • TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Examination is carried out as weekly submissions of assignments. If assignments have not been solved in a satisfactory way, a written examination is carried out.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web EQ2820

Offered by

Main field of study

Electrical Engineering

Education cycle

Second cycle

Add-on studies

No information inserted

Supplementary information

The course is given during period 4 every even year.

In this course, the EECS code of honor applies, see: http://www.kth.se/en/eecs/utbildning/hederskodex.