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I have two coordinate frames, A and B. I want to create the rotation matrix RAB which takes you from A to B. A is a right-handed system, and B is a left-handed system. Furthermore, after moving from a right- to a left-handed system, there is a further rotation. These two coordinate frames are illustrated in the image below.

As can be seen, it appears that the axes in B are simply the negative of the axes in A. So, my first attempt was to simply make these negative in the rotation matrix:

RAB = [-1 0 0, 0 -1 0, 0 0 -1]

(sorry -- I don't know how to write matrices properly here...)

However, after working through some examples, this did not work out.

Please could somebody answer either (or both!) these questions?

(a) Why does my above solution not hold? (b) what is the correct rotation matrix RAB?

enter image description here

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    \$\begingroup\$ Can you add an example that "did not work out"? (Expected vs. actual results...) \$\endgroup\$ – Marco13 Mar 3 '15 at 21:18
  • \$\begingroup\$ Here is an example where I'm confused about how to create a transformation matrix: math.stackexchange.com/questions/1174207/… \$\endgroup\$ – Karnivaurus Mar 3 '15 at 21:54
  • \$\begingroup\$ Moreover, I dont think that is rotation matrix, it looks like scaling matrix applying negative scale (result is mirroring) in all axes. But it should probably suit your needs - what is wrong with the result? \$\endgroup\$ – wondra Mar 3 '15 at 22:46

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