Lecturer(s)


Pech Pavel, prof. RNDr. CSc.

Hašek Roman, Mgr. Ph.D.

Course content

1. Vector space. Linear combination. 2. Linear dependence and independence of vectors. Basis of vector space. 3. Vector spaces with inner product. Orthogonal vectors. 4. Affine space. Affine subspaces. 5. The general equation of a hyperplane. Pencil and bundle of hyperplanes. 6. Relative position of affine subspaces. 7. Classification of relative positions of two affine subspaces. Transversals of skew subspaces. 8. Euclidean space. Cartesian coordinate system. Orthonormal basis. 9. Vector product. Generalization to Vn. 10. Outer product. Generalization to Vn. Volume of a simplex. 11. Distance between two subspaces. 12. Deviation between subspaces. 13. Application problems. 14. Summary

Learning activities and teaching methods

Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Demonstration

Learning outcomes

Vector spaces. Linear combination of vectors. Linear independence of vectors. Base. Vector spaces with inner product. Affine space and subspace. Relative positions of affine subspaces. Pencil and bundle of hyperplanes. Transversals of skew subspaces. Euclidean space. Vector product. Outer product. Distance of subspaces, the volume of simplex, the deviation of subspaces.
A graduate will understand basic terms from Linear algebra and their geometric interpretations within the range of the curriculum of the subject. She will learn to apply matrices and determinants on the investigation of relative positions of point subspaces.

Prerequisites

Knowledge of the basic properties of matrices and determinants. Corresponding computational skills with matrices and determinants. Solving of systems of linear equations skills.

Assessment methods and criteria

Combined exam
Active participation on seminars. Written and oral examination of knowledge in the range of the course.

Recommended literature


Bican, L.:. Lineární algebra. Praha, SNTL, 1979.

Krieg  Vaňatová, L.:. Analytická geometrie lineárních útvarů. České Budějovice, PF JU, 1994.

Motl, L., Zahradník, M.:. Pěstujeme lineární algebru, 3. vyd. Praha : Univerzita Karlova v Praze, nakladatelství Karolinum, 2002.

Pech, P.:. Analytická geometrie lineárních útvarů. České Budějovice, PF JU, 2004.

Sekanina, M. a kol.:. Geometrie I., SPN, 1986.
