# Thread: Difference between base and ordered base

1. ## Difference between base and ordered base

I don't understand what is the difference between a base and an ordered base of a vectorial space. Can you give me an example of a base and ordered base over a same vectorial space, say $\displaystyle \mathbb{R}^2$?

2. Thank you for the link, but I've already read it before and it doesn't provide a concrete example as I'd like.
Say I have the base $\displaystyle \{ (0,1), (1,0) \}$ that generates $\displaystyle \mathbb{R}^2$ I think. Is it an ordered base? I'm not even sure it generates $\displaystyle \mathbb{R}^2$ but I think yes since I can write any vector of $\displaystyle \mathbb{R}^2$ as combination of the 2 vectors forming the base.

3. By the way, I update solution $\displaystyle W^{\perp} \cap W$ of last question due to some mistake.
Did you know ?

4. Originally Posted by math2009
By the way, I update solution $\displaystyle W^{\perp} \cap W$ of last question due to some mistake.
Did you know ?
Do you mean in this thread : http://www.mathhelpforum.com/math-he...ersection.html ?
Thank you for all your help!