Applications of Symmetric Circulant Matrices to Isotropic Markov Chain Models and Electrical Impedance Tomography

Abstract

Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major properties of symmetric circulants scattered through the literature. Second, we report two new applications of these matrices to isotropic Markov chain models and electrical impedance tomography on a homogeneous disk with equidistant electrodes. A new special function is introduced for computation of the Ohm’s matrix. The latter application is illustrated with estimation of the resistivity of gelatin using an electrical impedance tomography setup.