Vector spaces

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Code:	45772
ECTS:	5.0
Lecturers in charge:	prof. dr. sc. Dražen Adamović - Lectures prof. dr. sc. Goran Muić - Lectures prof. dr. sc. Ozren Perše - Lectures
Lecturers:	Josip Grgurić, mag. math. - Exercises dr. sc. Tomislav Gužvić - Exercises Ivana Vukorepa, mag. math. - Exercises
English level: 1,0,0	All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

Load:

1. komponenta

Lecture type Total

Lectures 30

Exercises 30

* Load is given in academic hour (1 academic hour = 45 minutes)

Description:

COURSE AIMS AND OBJECTIVES: To explain basic results about linear operators on finite dimensional vector spaces (Jordan form, functional calculus, operators on inner product spaces).

COURSE DESCRIPTION AND SYLLABUS:
1. Linear operators on finite dimensional spaces
2. Dual spaces
3. Spectrum, characteristic and minimal polynomial
4. Nilpotent operators
5. Fitting decomposition
6. Jordan form
7. Functional calculus
8. Resolvent
9. Geometry of inner product spaces
10. The adjoint operator
11. Normal operators
12. Normal operators on real inner product spaces
13. Selfadjoint operators, Positive operators and polar decomposition

Literature:

S. Kurepa: Konačnodimenzionalni vektorski prostori i primjene
P. R. Halmos: Finite dimensional vector spaces
J. S. Gollan: The Linear Algebra a Beginning Graduate Student Ought to Know, Kluwer Texts in the Mathematical Sciences, vol. 27

1. semester

Algebra i osnove matematike - Regular study - Mathematics and Computer Science Education

2. semester

Algebra i osnove matematike - Regular study - Mathematics and Computer Science Education

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All activities regarding this course can be seen on Merlin platform. All notices and course related materials will be available on Merlin.

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Vector spaces

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