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. 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.
Source
Cumhuriyet Üniversitesi Fen-Edebiyat Fakültesi Fen Bilimleri DergisiVolume
21Issue
2URI
http://www.trdizin.gov.tr/publication/paper/detail/TXpRMU1UWTI=https://hdl.handle.net/20.500.12418/1257
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