You are in my class, it appears. Unless our lecturer steals his questions from elsewhere.
Section 23.4 in his notes cover this question pretty much perfectly.
I got this question in my Group Theory class and I'm not really sure how to go about it because I never really understood quaternions in the first place!
Let v be the unit vector ( )
and let R be the rotation through angle anticlockwise around Ov
Calculate R(1,0,0) by conjugating a quaternion.
Thanks for any help you can give me!
P.S. That one in the first part of the vector should be on top, I couldn't get the MATH tags to wrok properly
The problem with that is that I have no idea where to start. I don't know how to calculate a unitary matrix from a quaternion (in actuality I have no idea how to form ANY matrix from a quaternion) and so without that basic knowledge can do no work. It's fairly elementary. I'm not asking for the answer to the question, just a piece of basic knowledge from which I can do some work.
Every rotation of , given by the axis u and the angle of rotation , is the result of conjugation by unit quaternions (see here). Now you have , , and in the link. Can you proceed from here?
Note also that unit quarternions described by matrix (a+bi,c+di;-c+di,a-bi)=a1+bi+cj+dk, where 1=(1,0;0,1), i=(0, -1;1,0), j=(0, -i;-i,0), k=(i,0;0,-i) forms a group under multiplication which is isomorphic to SU(2) (see here).