Some results on the spectral decomposition of the axial m-index assignment problem

Abstract

In this paper, axial m-index assignment problem is reformulated as a linear programming problem and several algebraic characterizations of the coefficient matrix A of its problem are derived from known characterizations for singular value decomposition of a matrix. It is then shown that eigenvectors of the matrix $A^{+}A$ are characterized in terms of eigenvectors of the matrix $AA^T$, where $A^{+}$ is the Moore-Penrose inverse and $A^T$ is the transpose of the matrix A.