(Under construction) 

 I write this section for people ready to enter deeply in the maths. I will do it mainly with Geometric Algebra, which is better adapted than matrix algebra for dealing with rotations. 

 I had a difficult discussion with Guentherwagner on the point of determining if successive Euler rotations can be considered being well defined mathematical operators without taking in account the true position of the successive rotation axes, or what is the same thing without attaching each rotation matrix to a specific frame. If the answer is yes can we say that they commute, despite the fact that we know that rotations genrally do not commute ? 

 I tried to understand and perhaps modify the matricial quasi-demonstration in the text I critizised. The difficulty which renders that problem confusing is the fact that the simple matrices used give only a general indication on the rotation axis. If for instance you work with a simple matrix characterizing a rotation around OZ (with the number one in the lower right corner), you can apply it in any frame and thus choose arbitrarily your Z axis ... ! By the way, that explains the inverse order of the matrices in composing a combined Euler angle rotation. So I was perturbed by the fact that of course in matricial expressions we have . But as the matrices on both sides are in fact applied to different frames it gives in operator notation . That could be, but not so easily, expressed in matrix formulation. A contrario Geometric Algebra is particularly adapted to that task, and will perhaps reserve us a surprise.