MB003 Linear Algebra and Geometry I

Faculty of Informatics
Spring 2008
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor)
prof. Dr. rer. nat. RNDr. Mgr. Bc. Jan Křetínský, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Faculty of Informatics
Timetable
Fri 11:00–12:50 D2
  • Timetable of Seminar Groups:
MB003/01: Fri 14:00–15:50 B007, J. Paseka
MB003/02: Mon 10:00–11:50 B007, J. Křetínský
MB003/03: Tue 10:00–11:50 B003, D. Kruml
MB003/04: Tue 12:00–13:50 B003, D. Kruml
Prerequisites (in Czech)
! MB102 Mathematics II &&!NOW( MB102 Mathematics II )
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 14 fields of study the course is directly associated with, display
Course objectives
The course is concerned with the fundamentals of linear algebra and geometry. The main part of the course is devoted to matrices, systems of linear equations and linear maps.
Syllabus
  • Scalars, vectors and matrices: Properties of real and complex numbers, vector spaces and their examples, $R^n$ and $C^n$, multiplication of matrices, systems of linear eguations, Gauss elimination, computation of inverse matrices.
  • Vector spaces - basic notions: Linear combinations, linear independence, basis, dimension, vector subspaces, intersections and sums of subspaces, coordinates.
  • Linear mappings: Definition, kernel and image, linear isomorphism, matrix of linear mapping in given bases, transformation of coordinates.
  • Systems of linear equations: Properties of sets of solutions, rank a matrix, existence of solutions.
  • Determinants: Permutations, definition and basic properties of determinants, computation of inverse matrices, application to systems of linear equations.
  • Affine subspaces in $R^n$: Definition, parametric and implicit description, affine mapping.
  • Scalar product in $R^n$: Definition and basic properties of scalar product
Literature
  • Zlatoš, Pavol. Lineárna algebra a geometria. Předběžná verze učebních skript MFF UK v Bratislavě.
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods (in Czech)
Bude vyžadováno početní i teoretické zvládnutí přednesené látky (porozumění základním pojmům a větám, jednoduché důkazy).
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012.
  • Enrolment Statistics (Spring 2008, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2008/MB003