linear manifold
DefinitionSuppose is a vector space and suppose that is anon-empty subset of . If there exists a such that is a vector subspace of , then is a linear manifold of . Then wesay that the dimension
of is the dimension of and write .In the important case , is called a hyperplane.
A linear manifold is, in other words, a linear subspace that has possibly beenshifted away from the origin.For instance, in examples of linearmanifolds are points, lines (which are hyperplanes), and itself.In hyperplanes naturally describe tangent planes to a smoothhyper surface.
References
- 1 R. Cristescu, Topological vector spaces
,Noordhoff International Publishing, 1977.