In this paper, we give some results on the spectral deconposition and generalized inverse of the matrİK A whidı is the coeffident maJrix of the axial three-index assignment problem and investigate relations between eigenvalues and eigenvectors of the matrices and I-A' A where A’^ 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 ofthe eigenvectors oft he matrix AA7