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 $AA^T$ . 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 $AA^T$ .
Source
Communications Series A1: Mathematics and StatisticsVolume
49Issue
1-2URI
http://www.trdizin.gov.tr/publication/paper/detail/TXpNM056RXg=https://hdl.handle.net/20.500.12418/1063
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