autumn 2018

## SMN6190 Linear Algebra 2 - 5 ECTS

## Course content

- Particular and general vector spaces
- Basis and subspaces
- Inner product spaces
- The Gram-Schmidt process
- Least-squares problems
- Extension of the theory of eigenvalues and eigenvectors
- Diagonalization with generalizations
- Singular value decompositions
- Linear transformations with matrix representation

## Objectives of the course

**Knowledge (K):**

After completing the linear algebra course the candidate:

- Has advanced knowledge of concepts within linear algebra.
- Has thorough knowledge of central theories and methodologies within the listed concepts in linear algebra and know how to apply these in mathematical problems.
- Can analyse formulated linear algebra problems and identify methods to solve these.

**Skills (S):**

After completing the linear algebra course the candidate:

- Can recognize and identify linear problems and formulate them in terms of linear systems.
- Can analyse and deal critically with theories in linear algebra and use these to structure and formulate scholarly arguments.
- Can utilise existing interpretations and relevant methods within the field to accomplish a task.
- Can use relevant methods within the field.

**General competence (GC):**

After completing the linear algebra course the candidate:

- Can analyse relevant linear problems.
- Can apply the knowledge and skills within linear algebra to carry out assignments.
- Can communicate about different aspects in linear algebra, particularly explaining in mathematical terms how to deal with mathematical tasks.
- Can use the knowledge for concepts, theories and methods in linear algebra in other engineering areas.

**Teaching and Learning Methods**: The course is taught intensively during two non-consecutive weeks, in which a combination of lectures followed by task solving sessions and flipped classroom arrangements are used. All lectures are streamed and recorded. Videos provided in flipped classroom arrangements are made available to all students attending the course.

**Workload**: Two distributed assignments are to be completed. An obligatory questionnaire must be completed, in which students are encouraged to reflect on their learning goals in the course. Form of assessment: A final summative exam. Selected solutions from the exam will be graded externally.

## Date for examination

Written examination 12.10.2018The date for the exam can be changed. The final date will be announced in the StudentWeb early in May and early in November.

## Schedule

## Recommended reading/syllabus

David Lay: Linear Algebra and Its Applications, latest edition. Selected additional literature from textbooks: - G. Strang: Linear algebra and its applications - H. Anton: Elementary linear algebra Compendia: 'Linear systems, matrices and determinants', 'Real eigenvalues and eigenvectors Lecture notes, recorded lectures, provided videos and task solutions

Additional literature

G. Strang: Linear algebra and its applications

H. Anton: Elementary linear algebra

E. Kreyszig: Advanced engineering mathematics.