Many properties of physical systems can be expressed by symmetric matrices of order n, where n is the number of components in the system. The computer storage requirement for inverting the most general symmetric matrix is n(n+1)/2 storage locations. For large values of n, the number of multiplications required is proportional to n3. If the physical system possesses certain geometrical symmetries, both the amount of storage and the number of multiplications can be reduced substantially. It will be shown that if the physical system possesses p orthogonal planes of symmetry, where p = 1, 2, or 3, and if n is sufficiently larger, then the storage requirement can be reduced approximately by 1/2p and the number of multiplications by 1/4p.
Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.