Eigensolution of specially structured matrices with hyper-symmetry

Recently, four canonical forms have been developed and applied to the dynamics and stability analysis of symmetric frames. In this paper, hyper-symmetric matrices and specially structured matrices are defined and efficient methods are proposed for the eigensolution of such matrices. Applications are extended to hyper-graphs and specially structured graphs. Simple methods are developed for calculating the eigenvalues of the Laplacian matrices of such graphs. The developments presented in this paper can also be considered as generalization of Form II and Form III symmetry, previously defined by the authors