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
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Content and learning outcomes
- Repetition of vector spaces, inner product, determinant, rank
- Eigenvalues, eigenvectors and characteristic polynomials
- Unitary equivalence, QR-factorisation
- Canonical forms, Jordan form, polynomials and matrices
- Hermitian and symmetric matrices, variational characterisation of eigenvalues, simultaneous diagonalisation
- Norms for vectors and matrices
- Localisation and disturbance of eigenvalues
- Positive definite matrices. Singular value decomposition
- Nonnegative matrices, positive matrices, stochastic matrices
- Stable matrices; Liapunov's theorem
- Matrix equations, Kronecker product and Hadamard product
- 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
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.
Good knowledge of first course in linear algebra. Admission is by request to examiner.
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.
- 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
Opportunity to raise an approved grade via renewed examination
- 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 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
Main field of study
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.