What Are Canonical Coordinates and How to Convert a Basis in R^2?

[bullsangelsra]

What are canonical coordinates?
Im trying to convert a basis of R^2 into canonical coordinates but i do not know what they are. Are they the ones such as: e1, e2, and e3

 

[LukeD]

Yes, according to Wikipedia, the canonical basis of R^n is another word for the standard basis. (e_1, e_2, ..., e_n)

So if you had a vector in terms of your basis, you'd just have to rewrite it in terms of the standard basis.

 

[bullsangelsra]

good, thanks, okay...
so if A= ([ 1] [1])
...([-1],[1])
and is a basis of R^2 how would i convert this into canonical coordinates?