A rank characterization of the number of final classes of a nonnegative matrix |
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Authors: | Uriel G Rothblum |
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Institution: | Yale University School of Organization and Management 52 Hillhouse Avenue New Haven, Connecticut 06520 USA |
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Abstract: | Let A be a nonnegative square matrix, and let D be a diagonal matrix whose iith element is , where x is a (fixed) positive vector. It is shown that the number of final classes of A equals n?rank(A?D). We also show that null(A?D) = null(A?D)2, and that this subspace is spanned by a set of nonnegative elements. Our proof uses a characterization of nonnegative matrices having a positive eigenvector corresponding to their spectral radius. |
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