Syllabus
Groups of linear mappings
Linear forms, Bilinear and quadratic forms
Transition matrix and change of basis
Orthogonalization
Euclidean vector space, isometry classification in E3, isometry representation in En
Similar transformation in En
Affine transformation in En
Projective extension of an affine space; Projective space, projective transformation
Projective classification of quadrics
Affine classification of quadrics
Metric classification of quadrics
Annotation
This follow-up course to Linear Algebra and Geometry is focused on the classification of geometric spaces based on the invariants of linear representations. Knowledge is used to classify quadrics according to their projective, affine, and metric properties.
The acquired knowledge and skills belong to the parts needed for other mathematics courses and are needed for teaching high school analytic geometry.