Ways to represent subspaces of a vector space

I never thought that Google would yield such a horrific lack of
information on this subject, and yet it does.

What are some good and unique ways to notate a subspace of a vector space?

A few that come to mind:
1) A matrix in RREF form
2) A canonical choice of multivector representing that space
3) A projection map
4) A saturated matrix in Hermite form
5) Perhaps a generalization of Miller indices, as used in crystallography

Any others that anyone knows about? I find something lacking in each
of these, personally - sometimes it's not clear what space is being
represented (like wedgies), sometimes it's hard to work these things
out by hand (like saturated Hermite form matrices), sometimes both
(like Frobenius projection maps).

-Mike