淡江大學機構典藏:Item 987654321/41400
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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/41400


    Title: The Perron generalized eigenspace and the spectral cone of a cone-preserving map
    Authors: 譚必信;Tam, Bit-shun
    Contributors: 淡江大學數學學系
    Keywords: Cone-preserving map;Nonnegative matrix;Level characteristics;Height characteristic;Semi-distinguished invariant face;Perron generalized eigenspace;Principal component;Spectral cone;Preferred-basis theorem;Majorization relation
    Date: 2004-12-01
    Issue Date: 2010-01-28 07:28:53 (UTC+8)
    Publisher: Elsevier
    Abstract: A unified treatment is offered to reprove known results on the following four highlights of the combinatorial spectral theory of nonnegative matrices, or to extend (or partly extend) the results to the setting of a linear map preserving a polyhedral proper (or proper) cone: the preferred-basis theorem, equivalent conditions for equality of the (graph-theoretic) level characteristic and the (spectral) height characteristic, the majorization relation between the two characteristics, and the relation between the combinatorial properties of a nonnegative matrix and the positivity of the individual entries in its principal components. This is achieved by employing the new concept of spectral cone of a cone-preserving map and combining the cone-theoretic methods developed in our previous papers on the geometric spectral theory of cone-preserving maps with the algebraic–analytic method introduced by Hartwig, Neumann and Rose and further exploited by Neumann and Schneider for nonnegative matrices.
    Relation: Linear Algebra and Its Applications 393(1-3), pp.375-429
    DOI: 10.1016/j.laa.2004.08.020
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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