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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41378

    Title: On the distinguished eigenvalues of a cone-preserving map
    Authors: Tam, Bit-Shun
    Contributors: 淡江大學數學學系
    Date: 1990-04
    Issue Date: 2013-06-13 11:25:26 (UTC+8)
    Publisher: Philadelphia: Elsevier Inc.
    Abstract: We generalize many known results on a nonnegative matrix concerning linear inequalities, Collatz-Wielandt sets, and generalized eigenvectors to the setting of a matrix preserving a (finite-dimensional) proper cone. A simple cone-theoretic proof is given for the nonnegative-basis theorem for the algebraic eigenspace of a nonnegative matrix. The result is also extended to a matrix preserving a polyhedral cone. Given proper cones K1 and K2 in different euclidean spaces, a necessary and sufficient condition is also obtained for the existence of a nonzero matrix X which takes K2 into K1 and satisfies AX = XB, where A, B are given matrices preserving K1 and K2 respectively. This extends and answers a recent open question posed by Hartwig.
    Relation: Linear Algebra and Its Applications 131(C), pp.17-37
    DOI: 10.1016/0024-3795(90)90372-J
    Appears in Collections:[數學學系暨研究所] 期刊論文

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