# Linear Algebra

## Course description

Lectures:

1. Basic operations with vectors,
2. Operations with matrices,
3. Systems of linear equations,
4. Vector spaces,
5. Orthogonal projections and overdetermined systems,
6. Symmetric and orthogonal matrices,
7. Determinants,
8. Eigenvalues and eigenvectors

Lab practice:

Support of the theoretical knowledge by practical examples

Study of examples relevant for the computer science and informatics students

At the lab practice sessions students will individually solve problems under the supervision of an assistant.

Homeworks:

Homework assignments are obligatory and provided in a weekly rhythm, but less time demanding. The purpose of homework is to prepare students to prompt study of the subject. Students can solve homeworks either individually or collectively. The contents of homework topics are usually following contact hours.

## Objectives and competences

The course aims to acquaint students with the methods of linear algebra, and train them to use these methods in solving problems in various areas of computer science.

## Learning and teaching methods

Lectures, lab practice, homeworks

## Intended learning outcomes

After successfully completing the course, the students will be able to:

-know and use basic objects (scalars, vectors, matrices) and the relationships between them,

-perform basic operations over them, and understand the properties of these operations,

– apply methods of linear algebra to solving problems arising in other fields (computer science, science, engineering),

-realize that the same methods can be used in solving various concrete examples in the field of modelling various phenomena with computers,

-use of abstraction of linear algebra and linear  systems to model and solve specific problems.

## Reference nosilca

• OBLAK, Polona. The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix. Linear multilinear algebra, 2008, vol. 56, no. 6, str. 701-711.
• DOLŽAN, David, OBLAK, Polona. Invertible and nilpotent matrices over antirings. Linear algebra appl., 2009, vol. 430, iss. 1, str. 271-278.
• KOŠIR, Tomaž, OBLAK, Polona. On pairs of commuting nilpotent matrices. Transform. groups, 2009, vol. 14, no. 1, str. 175-182.
• DOLINAR, Gregor, GUTERMAN, Aleksandr Èmilevič, KUZMA, Bojan, OBLAK, Polona. Extremal matrix centralizers. Linear Algebra and its Applications, 2013, vol. 438, iss. 7, str. 2904-2910.
• OBLAK, Polona, ŠMIGOC, Helena. The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph. Linear Algebra and its Applications, 2017, vol. 512, str. 48-70.

Celotna bibliografija je dostopna na SICRISu:

http://sicris.izum.si/search/rsr.aspx?lang=slv&id=6758

## Study materials

1. Bojan Orel: Linearna algebra, Založba FRI, 2017, dostopno na http://matematika.fri.uni-lj.si/LA/lapdf.
2. Gilbert Strang, Introduction to Linear Algebra, Cambridge press, 2003.
3. David Poole: Linear Algebra, A Modern Introduction, Brooks/Cole, 2011.

Aleksandra Franc: Rešene naloge iz linearne algebre, 2019, dostopno na http://matematika.fri.uni-lj.si/la/la_zbirka.pdf.

## Bodi na tekočem

Univerza v Ljubljani, Fakulteta za elektrotehniko, Tržaška cesta 25, 1000 Ljubljana