Thank you very much for you reply. You stated the problem more clearly than I did.
From the initial conditions (2.) I can define immediately three components of new basis vectors ( A{\bf i}_x = acos(\alpha), A{\bf j}_y = acos(\beta), A{\bf k}_z = acos(\gamma)).
For the rest of components...
Hello,
I would like to rotate the Cartesian coordinate system ( i=(1,0,0); j=(0,1,0); k=(0,0,1) ) so that angles between new and the old axes be equal to α, β and γ, respectively. Is any simple way similar to the Euler transformations to accomplish that?