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EQ2820 Matrix Algebra, Accelerated Program 7.5 credits

Matrisalgebra, forskarförberedande

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).

  • Educational level

    Second cycle

  • Academic level (A-D)

    D

  • Subject area

    Electrical Engineering

  • Grade scale

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

Course offerings

Spring 14 for programme students

Learning outcomes

The course is given every second year and is suitable as a first postgraduate (Ph.D) course or as an advanced course in the final year of the M.Sc. program (e.g., for students considering to join the PhD program).

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. It assumes some familiarity with basic concepts from linear algebra (as can be expected by good knowledge from undergraduate studies).

Learning outcomes:

After the course, each student is expected to be able to:

  • Show a good working knowledge of some fundamental tools (specified by the course content) in matrix algebra.
  • Use the acquired knowledge to more easily apprehend research papers in engineering.
  • Identify research problems in which matrix algebra tools may be powerful.
  • Apply the knowledge to solve the identified matrix algebra problems.
  • Combine several sub problems and solutions to solve more complex problems.

Course main content

Main contents:

1. Review of vector spaces, inner product, determinants, rank

2. Eigenvalues, eigenvectors characteristic polynomial

3. Unitary equivalence QR-factorization

4. Canonical forms Jordan form, polynomials and matrices

5. Hermitian and symmetric matrices Variational characterization of eigenvalues, simultaneous diagonalization

6. Norms for vectors and matrices

7. Location and perturbation of eigenvalues

8. Positive definite matrices. Singular value decomposition

9. Nonnegative matrices, positive matrices, stochastic matrices

10. Stable matrices; Lyapunovs theorem

11. Matrix equations and the Kronecker product, Hadamard product

12. Matrices and functions square roots, differentiation

Eligibility

For single course students: 180 credits and documented proficiency in English B or equivalent

Prerequisites

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

Literature

Will be reported on the course homepage four weeks before start.

Previously we have used the books “Matrix Analysis” and “Topics in Matrix Analysis” by R.A. Horn and C. R. Johnson.

Examination

  • TEN1 - Examination, 7.5 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

Weekly homework assignments (TEN1, 7.5 ECTS credits, grading A-F)
Written exam if homework not solved satisfactorily.

Offered by

EES/Signal Processing

Contact

Magnus Jansson

Examiner

Magnus Jansson

Supplementary information

The course is given every second year (see course homepage). Given period 4 spring 2010.

Version

Course plan valid from: Autumn 07.
Examination information valid from: Autumn 07.