Syllabus
Vektorové prostory nad tělesem a jejich podprostory, Vlastnosti vektorových prostorůMatice nad tělesem, jejich vlastnosti a operace s nimiDeterminant čtvercové matice, metody výpočtuLineární zobrazení Afinní bodový prostor a jeho podprostory, Afinní zobrazení v E2Eukleidovský prostor, shodné zobrazení v E2 Podobné zobrazení v E2Popis a zkoumání útvarů v E2 a E3 analyticky
Annotation
Elementary course on vector spaces, matrices, linear equations, determinants, and linear transformations with an emphasis on geometric interrelations. The aim of the subject is to introduce participants to elementary parts of algebra, theoretical arithmetic, and analytic geometry, on which the school mathematics is based. Methods presented in the subject are necessary for further mathematical disciplines included in teachers' education.
Vector spaces over a field and their subspaces, Properties of vector spaces
Matrices over a field, their properties, and operations on them
Determinant of a square matrix, methods of calculation
Linear transformation
Affine point space and its subspaces, Affine transformations in E2
Euclidean space, isometries in E2
Similarities in E2
Analytic description and examination of objects in E2 and E3