## M003 Linear Algebra and Geometry I

Faculty of Informatics
Autumn 2000
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)
Mgr. Richard Lastovecki (seminar tutor)
Mgr. Hynek Mlčoušek (seminar tutor)
RNDr. Blanka Sedlačíková, Ph.D. (seminar tutor)
Mgr. Ivan Sobotík (seminar tutor)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
doc. Mgr. Vojtěch Žádník, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Departments - Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites (in Czech)
NOW ( M003c Linear Algebra and Geometry I ) && (! 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
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