M503 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
M503/P1: Tue 9:00–11:50 UKP
M503/P2: Thu 9:20–11:50 UKP
M503/P3: Thu 17:00–19:50 D2
Prerequisites (in Czech)
NOW(M503c Linear Algebra and Geometry I - seminar) && (!M003 Linear Algebra and Geometry I) && (!NOW(M003 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
  • Zlatoš, Pavol. Lineárna algebra a geometria. Předběžné učební texty MFF UK v Bratislavě.
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita,1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Method of verifying learning outcomes and course completion requirements (in Czech)
Bude vyžadováno početní zvládnutí přednesené látky.
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 1999, Autumn 2000.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2001/M503