M003 Linear Algebra and Geometry I

Faculty of Informatics
Autumn 2001
Extent and Intensity
3/2. 5 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
doc. RNDr. Martin Čadek, CSc. (lecturer)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable of Seminar Groups
M003/P1: Tue 9:00–11:50 UKP
M003/P2: Thu 9:20–11:50 UKP
M003/P3: Thu 17:00–19:50 D2
Prerequisites (in Czech)
NOW(M003c Linear Algebra and Geometry I) && (!M503 Linear Algebra and Geometry I) && (!NOW(M503 Linear Algebra and Geometry I))
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
Key topics
  • 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.
Study resources and literature
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
  • Zlatoš, Pavol. Lineárna algebra a geometria. Předběžná verze učebních skript MFF UK v Bratislavě.
Method of verifying learning outcomes and course completion requirements (in Czech)
Bude vyžadováno početní i teoretické zvládnutí přednesené látky (porozumění základním pojmům a větám, jednoduché důkazy).
Language of instruction
Czech
Follow-Up Courses
Teacher's information
http://www.math.muni.cz/~cadek
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 1995, Autumn 1996, Autumn 1997, Autumn 1998, Autumn 1999, Autumn 2000, Spring 2003.
  • Enrolment Statistics (Autumn 2001, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2001/M003