The 4 x 4 system matrix is applied to corrected astigmatic systems including a schematic eye in which each surface is astigmatic at a different axis. In addition to representing the eye, the 4 x 4 system generates 2 x 2 magnification matrices which describe the meridional magnifications that occur in the presence of astigmatism including the magnifications that occur with bitoric eikonic correcting lenses, or other meridional magnifying systems.