My question is about applying rules of quaternions to quaternion matrices.
I know that for some rotation quaternion
q = [w, x, y, z], I can find the rotation of point
p2 = q*p1*conjugate(q). I also know that I can do quaternion multiplication to get the combined rotation of 2 quaternions
q2 by using quaternion multiplication
q = q1*q2 as expressed here.
Now suppose I construct a quaternion matrix as described here. Furthermore suppose I do that for three coordinate axes to construct three quaternion matrices
Qz. Could I then get a combined quaternion matrix to achieve the same result by doing
Q = Qz*Qy*Qx and then applying that to
p2 = Q*p1)? Obviously the ordering here matters.
This is somewhat similar to this question, but I am specifically interested in knowing if the method I have shown produces the correct result. This question is also not about whether or not this approach is the preferred way to do it.
This question has some nice references, but I didn't find the answer to what I'm asking at any of the links.