Dimension of subspace

  • Thread starter dan0
  • Start date
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
What does non-trivial mean here? With "my" usage of non-trivial, I'd say it's not possible. Because if V is a finite-dimensional vector space and W is a subspace of V with dim(W) = dim(V), then V = W (this uses the fact that n linearly independent vectors in an n-dimensional space must necessarily form a basis of the space). Maybe it's possible with a space of infinite dimension, though.
Last edited:


Science Advisor
Homework Helper
yep. take polynomials of even degree, as a subspace of all polynomials. does that work?

Want to reply to this thread?

"Dimension of subspace" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads