angle preserving transformations


by bigli
Tags: angle, preserving, transformations
bigli
bigli is offline
#1
Jul11-07, 08:07 AM
P: 16
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!!
Phys.Org News Partner Science news on Phys.org
Internet co-creator Cerf debunks 'myth' that US runs it
Astronomical forensics uncover planetary disks in Hubble archive
Solar-powered two-seat Sunseeker airplane has progress report
CompuChip
CompuChip is offline
#2
Jul11-07, 09:51 AM
Sci Advisor
HW Helper
P: 4,301
Try looking up Hermitian operators somewhere.


Register to reply

Related Discussions
Preserving trees organizations General Discussion 1
Order-preserving injection Calculus & Beyond Homework 1
angle preserving linear transformations Linear & Abstract Algebra 1
Measure-preserving flow Differential Equations 7
orientation preserving and determinants Linear & Abstract Algebra 4