# Subspace

A subset W of R^{n} is a subspace of R^{n} if:

- the zero vector is in W;
- x+y is in W whenever x and y are in W; and
- ax is in W whenever x is in W and a is any scalar.

**See also: **Dimension of a Subspace, Orthogonal Complement of a Subpace.

**Subjects: ** Algebra