Geometric Description
Geometrically, a subspace of Rn is simply a flat through the origin, i.e. a copy of a lower dimensional (or equi-dimensional) Euclidean space sitting in n dimensions. For example, there are four different types of subspaces in R3:
- The singleton set { (0, 0, 0) } is a zero-dimensional subspace of R3.
- Any line through the origin is a one-dimensional subspace of R3.
- Any plane through the origin is a two-dimensional subspace of R3.
- The entire set R3 is a three-dimensional subspace of itself.
In n-dimensional space, there are subspaces of every dimension from 0 to n.
The geometric dimension of a subspace is the same as the number of vectors required for a basis (see below).
Read more about this topic: Euclidean Subspace
Famous quotes containing the words geometric and/or description:
“New York ... is a city of geometric heights, a petrified desert of grids and lattices, an inferno of greenish abstraction under a flat sky, a real Metropolis from which man is absent by his very accumulation.”
—Roland Barthes (1915–1980)
“It [Egypt] has more wonders in it than any other country in the world and provides more works that defy description than any other place.”
—Herodotus (c. 484–424 B.C.)