Form Invariance under Rotation about the 3-axis

Stiffness and compliance matrices in compact form are rotated with Bond transformations (Auld, 1990). If we look at the Bond forms for rotation about the 3-axis we see that they have the identical block diagonal structure of our stiffness matrix illustrated above. Since block matrices of the same shape form a group under matrix multiplication, this means that we can rotate monoclinic systems about the symmetry axis and leave the form unchanged. What this means physically is that the property that defines a monoclinic system, the two-fold symmetry, is not tied to azimuth in the symmetry plane.