Standard Monoclinic Form

In case of monoclinic systems, we recognize the one symmetry plane, the (12) plane and this leads to:  

$$\pmatrix{c_{11}&c_{12}&c_{13}&0&0&c_{16}\cr c_{12}&c_{22}&c... ... 0&0&0&c_{45}&c_{55}&0\cr c_{16}&c_{26}&c_{36}&0&0&c_{66}\cr}$$ (2)

Without loss of generality, and to simplify discussion, we now rearrange the rows and columns so that the 6th lie between the 3rd and 4th,  

$$\pmatrix{c_{11}&c_{12}&c_{13}&c_{16}&0&0\cr c_{12}&c_{22}&c... ...66}&0&0\cr 0&0&0&0&c_{44}&c_{45}\cr 0&0&0&0&c_{45}&c_{55}\cr}$$ (3)

and the stiffness matrix is now in block diagonal form.