Mirror-Symmetric matrices and their application

The well-known centrosymmetric matrices correctly reflect mirror-symmetry with no component or only one component on the mirror plane. Mirror-symmetric matrices defined in this paper can represent mirror-symmetric structures with various components on the mirror plane. Some basic properties of mirror-symmetric matrices were studied and applied to interconnection analysis. A generalized odd/even-mode decomposition scheme was developed based on the mirror reflection relationship for mirror-symmetric multiconductor transmission lines (MTLs). The per-unit-length (PUL) impedance matrix Z and admittance matrix Y can be divided into odd-mode and even-mode PUL matrices. Thus the order of the MTL system is reduced from n to k and k + p, where p (≥ 0) is the conductor number on the mirror plane. The analysis of mirror-symmetric matrices is related to the theory of symmetric group, which is the most effective tool for the study of symmetry.