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EQ2820 Matrix Algebra, Accelerated Program 7.5 credits

Administer About course

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).

Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

Application

For course offering

Spring 2024 Start 18 Mar 2024 programme students

Application code

60563

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.

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

Profile picture Magnus Jansson

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 room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

EECS/Intelligent Systems

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.