• Support PF! Buy your school textbooks, materials and every day products Here!

Unitary coordinate transformation = rotation?

  • Thread starter Pacopag
  • Start date
  • #1
197
4

Homework Statement


Suppose I define a linear coordinate transformation that I can describe with a matrix U.
If U is unitary. i.e.
[tex]U^{-1}U = UU^{-1}=1[/tex]
does that necessarily imply that the transformation corresponds to a pure rotation (plus maybe a translation), so that I may assume that volumes are invariant?


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
Yes, volumes are invariant, certainly. The jacobian is 1. There are no translations if the transformation is linear. There could be reflections.
 
  • #3
197
4
Thank you.
 

Related Threads for: Unitary coordinate transformation = rotation?

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
4
Views
1K
Replies
3
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
1
Views
1K
Top