I'd like to know how to get the rotation matrix for the transformation from one cartesian coordinate system `(X, Y, Z)` to another one `(X', Y', Z')`. 

Both systems are defined with three orthogonal vectors as one would expect. No scaling or translation occurs. I'm using *OpenSceneGraph* and it offers a `Matrix` convenience class, if it makes finding the matrix easier: 

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> <http://www.openscenegraph.org/documentation/OpenSceneGraphReferenceDocs/a00403.html>.
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