Spectral Decompositions and Generalized Inverses in a Circularization Network Flow Problem

In this paper, we give some algebraic results on the spectral decomposition and generalized inverse of A which is a coefficient matrix of a circularization network flow problem with m + n + 2 nodes and (m + 1)(n + 1) arcs, and investigate relations between eigenvalues and eigenvectors of the matrices AAT and A+A. It has been shown that the problem and its special case, the Hitchcock-Koopmans transportation problem, have common algebraic characterizations, where AT is the transpose and A+ is the generalized inverse of A.