Spectral decompositions and feasible directions in the axial three-index assigment problem

Abstract

In this paper, we give some results on the spectral decomposition and generalized inverse of the matrix A which is the coefficient matrix of the axial three-index assignment problem and investigate relations between eigenvalues and eigenvectors of the matrices $AA^T$ and $I-A^+A$ where $A^T$ is the transpoze and A+ is the generalized inverse of A. It has been shown that the feasible directions of the axial three-index assignment problem can be investigated in terms of the eigenvectors of the matrix $AA^T$ .