We propose that the height-angle ray vector in matrix optics should becomplex, based on a geometric algebra analysis. We also propose that the ray's2x2 matrix operators should be right-acting, so that the matrix productsuccession would go with light's left-to-right propagation. We express thepropagation and refraction operators as a sum of a unit matrix and an imaginarymatrix proportional to the Fermion creation or annihilation matrix. In thisway, we reduce the products of matrix operators into sums ofcreation-annihilation product combinations. We classify ABCD optical systemsinto four: telescopic, inverse Fourier transforming, Fourier transforming, andimaging. We show that each of these systems have a corresponding Lagrangetheorem expressed in partial derivatives, and that only the telescopic andimaging systems have Lagrange invariants.
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