Dimension of subspace

1. Jun 15, 2005

dan0

Hi,
I'm just learning for my linear algebra exam and I wonder if somebody could give me an example of a nontrivial subspace which has as many dimensions as the original space.
Thanks a lot

2. Jun 15, 2005

HallsofIvy

Staff Emeritus
What do you mean by "nontrivial". I would call a subspace nontrivial as long as it was not just the 0 vector. If that's the case then just take any vectors space V with V as the subspace.

Another possibility, a lot more non-trivial would be an infinite dimensional vector space with an infinite dimensional subspace.
The vector space of all polynomials with subspace the space of all even polynomials comes to mind.