Angle preserving transformations

  • Thread starter bigli
  • Start date
  • #1
16
0
If x,y of R^n (as a normed vector space) are non-zero, the angle between x and y, denoted <(x,y), is defined as arccos x.y/(|x||y|).
The linear transformation T :R^n----->R^n
is angle preserving if T is 1-1, and for x,y of R^n (x,y are non zero) we have
<(Tx,Ty) = <(x,y).

what are all angle preserving transformations T :R^N---->R^N ?

I guess that answering to this quastion is connected with eigenvalues of T.please help me!!
 
Last edited:

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
Try looking up Hermitian operators somewhere.
 

Related Threads on Angle preserving transformations

Replies
2
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
12
Views
4K
Replies
1
Views
1K
Replies
1
Views
2K
Replies
7
Views
6K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
17
Views
4K
Replies
0
Views
3K
Top