Syllabus
*Affine maps
- Ratios of vectors along a line and the parameter in the parametric equation of a line; properties.
- Affine map, basic properties, representation. Associated homomorphism.
- Affine transformations, invariant points and vectors. Affine group.
- Basic affine maps. Module of affine map, equiaffinity.
- Translation group, homothety group.
*Maps in Euclidean space
- Linear isometry, basic properties, representation.
- Classification of linear isometries in plane, reflections. Isometry group.
- Similarity map, basic properties, representation. Similarity as composition of a homothety and an orthogonal transformation. Similarity group.
- Circle inversion, basic properties, representation.
- Groups of geometrical transformations.
Annotation
Continuation of Geometry I. Study of geometrical transformations in affine and Euclidean space, their basic properties, equations, invariant points and directions.
The theory is based on linear algebra.