Thread: Rotation Matrix Help Needed

Hi, I have been working on a matrix problem that will probably be easy to most people reading this forum, but I have attempted to solve it via a lot of searches and brute force and cannot come up with the answer.

The question is, succinctly, how do I derive a rotation matrix relative to the identity matrix that is functionally equivalent to the rotation of another frame of reference?

So if I have a local frame of reference where UP is facing down the Z axis and within that frame I rotate 45 degrees along the heading, how could I derive a rotation that would perform a -45 degree bank rotation relative to a frame of reference where UP is up the Y axis?

Or are these the same transformations?

If anyone could help put me out of my misery, I'd appreciate it. Thanks.

Added:

I guess a related question would be: how do you express a vertex in local coordinate system in terms of another local coordinate system?

Ambi