## Coordinate System Transformations

Lets say I have Coordinate Frame's A and B.

and...

I have the coordinates of the 3 principle axes of B in terms of Frame A,

So for a simple example, a rotation of +pi/2 about the z axis of A would yield the following mapping of the xyz axes of B in terms of Frame A:

XA -> -YB
YA -> XB
ZA -> ZB

My question is: Given a slightly more complex mapping, but without knowledge of euler rotations, how could a Rotation Matrix be calculated?

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 Just look at how the standard basis vectors transform. Those are the columns of your rotation matrix. Also, for a change of coordinate systems, a rotation matrix need not exist (some changes are not rotations.)

 Quote by JeSuisConf Just look at how the standard basis vectors transform. Those are the columns of your rotation matrix. Also, for a change of coordinate systems, a rotation matrix need not exist (some changes are not rotations.)
Clean and simple, with the added bonus of triggering a very faint memory of learning that once.

Thanks so much for clearing it up, this is what I need for my application.

 Tags coordinate transfom, mapping, rotation matrix, solved