M003 Linear Algebra and Geometry I

Faculty of Informatics
Autumn 1999
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)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Mgr. Milan Sekanina, Ph.D. (lecturer)
Guaranteed by
Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
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
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.
Literature
  • 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). Zkouška se skládá z písemného testu uprostřed semestru, který má váhu 25 % a není možné jej opakovat, a z písemky ve zkouškovém období s váhou 75 %, kterou je možno jedenkrát opakovat, a z případného ústního zkoušení.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Autumn 1995, Autumn 1996, Autumn 1997, Autumn 1998, Autumn 2000, Autumn 2001, Spring 2003.
  • Enrolment Statistics (Autumn 1999, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn1999/M003