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Abstract
In this paper we determine the nonnegativity structure of the principal components of an n× nnonnegative matrix Pin terms of the marked reduced graph , the minus M-matrix which can be associated with P. We then apply this result to consider various types of nonnegative bases for the Perron eigenspace of P which can be extracted from a certain nonnegative matrix which is a polynomial in P. We also obtain a characterization for the eigenprojection Pon the Perron eigenspace of Pto be, itself, a nonnegative matrix. Our results provide new proofs and extensions of results of Friedland and Schneider and of Hartwig, Neumann, and Rose.
∗Dedicated to Henryk Minc on the occasion of his 70th birthday.
∗∗Work supported by U.S. Air Force Grant AFOSR-88-0047 and NSF Grant DMS-9007030. Part of this author's work was carried out while visiting the Sonderforschungsbereich 343 Diskrete Strulauren in der Mathematik, at the University of Bielefeld, Bielefeld, Germany.
†Work supported by NSF Grant DMS-8901445, by NSF Grant ECS-8718971, and by the Ministry of Education, Science and Culture, Japan.
∗Dedicated to Henryk Minc on the occasion of his 70th birthday.
∗∗Work supported by U.S. Air Force Grant AFOSR-88-0047 and NSF Grant DMS-9007030. Part of this author's work was carried out while visiting the Sonderforschungsbereich 343 Diskrete Strulauren in der Mathematik, at the University of Bielefeld, Bielefeld, Germany.
†Work supported by NSF Grant DMS-8901445, by NSF Grant ECS-8718971, and by the Ministry of Education, Science and Culture, Japan.
Notes
∗Dedicated to Henryk Minc on the occasion of his 70th birthday.
∗∗Work supported by U.S. Air Force Grant AFOSR-88-0047 and NSF Grant DMS-9007030. Part of this author's work was carried out while visiting the Sonderforschungsbereich 343 Diskrete Strulauren in der Mathematik, at the University of Bielefeld, Bielefeld, Germany.
†Work supported by NSF Grant DMS-8901445, by NSF Grant ECS-8718971, and by the Ministry of Education, Science and Culture, Japan.