# [SOLVED] linear transformation question

• Jul 25th 2005, 02:01 PM
tricky hornet
[SOLVED] linear transformation question
can anyone tell me this, it's driving me crazy because it should be easy. here goes.
For a roation of the vector (x,y,z) ( in 3-space obviously) about an axis which is determined by an arbitrary unit vector U=(a,b,c) through a positive angle beta(@), prove that that transformation Matrix is defined as

[HTML] a^2(1-cos@)+cos@ ab(1-cos@)-csin@ ac(1-cos@)+bsin@

ab(1-cos@)+csin@ b^2(1-cos@)+cos@ bc(1-cos@)-asin@

ac(1-cos@)-bsin@ bc(1-cos@)+asin@ c^2(1-cos@)+cos@ [/HTML]
• Jul 27th 2005, 01:04 AM
Rebesques
what?
I tried a little net search, and came up with

http://mathworld.wolfram.com/RotationFormula.html

I put n=U and r=(x,y,z), and after some brief computations, formula (3) of that page is exactly r'=Ar, where A is the matrix given.

Tell me if the derivation of the formula seems difficult (...not that I will be able to help :P)

http://mathworld.wolfram.com/images/...ionFormula.gif