At the end of the course students should be able to solve standard problems in general Euclidean space including relative positions, distances, and deviations of affine subspaces.
Affine spaces and subspaces. Parametric and general expressions of affine subspaces. The notion of parallelism, relative positions. Half-spaces and convex hulls. Euclidean spaces. Inner product and the notion of perpendicularity. Exterior and vector product, Gramm determinant, volumes. Distances and deviations of subspaces.