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

  • Context: Undergrad 
  • Thread starter Thread starter bullsangelsra
  • Start date Start date
  • Tags Tags
    Coordinates
Click For Summary
SUMMARY

Canonical coordinates refer to the standard basis in R^n, specifically represented as e1, e2, ..., en. In the context of converting a basis in R^2 to canonical coordinates, one must express the given vector in terms of the standard basis. For example, if A is defined as a basis in R^2 with vectors ([1, 1], [-1, 1]), the conversion process involves rewriting these vectors using the canonical basis vectors.

PREREQUISITES
  • Understanding of vector spaces in linear algebra
  • Familiarity with basis and dimension concepts
  • Knowledge of standard basis vectors in R^n
  • Ability to perform vector transformations and linear combinations
NEXT STEPS
  • Study the properties of vector spaces and linear independence
  • Learn about basis transformations in linear algebra
  • Explore the concept of linear combinations and their applications
  • Practice converting between different bases in R^2 and R^3
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, as well as anyone involved in fields requiring vector space analysis and transformations.

bullsangelsra
Messages
5
Reaction score
0
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
 
Physics news on Phys.org
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.
 
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?
 

Similar threads

  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 27 ·
Replies
27
Views
3K
  • · Replies 6 ·
Replies
6
Views
6K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 9 ·
Replies
9
Views
3K