A novel elementary algorithm for solving comrade linear systems

Recently, three computational algorithms for solving comrade linear systems have been proposed by Karawia (2013, 2007) [6,5] and by Sogabe (2008) [10]. In this paper, we derive a novel elementary algorithm for solving comrade linear systems based on matrix reordering and the Sherman-Morrison-Woodbury formula. An efficient method of evaluating the determinant of a comrade matrix is also discussed.