English  |  正體中文  |  简体中文  |  全文笔数/总笔数 : 53018/88142 (60%)
造访人次 : 9559573      在线人数 : 65
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library & TKU Library IR team.
搜寻范围 查询小技巧:
  • 您可在西文检索词汇前后加上"双引号",以获取较精准的检索结果
  • 若欲以作者姓名搜寻,建议至进阶搜寻限定作者字段,可获得较完整数据
  • 进阶搜寻

    jsp.display-item.identifier=請使用永久網址來引用或連結此文件: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41386

    题名: Cross-positive matrices revisted
    作者: Gritzmann, Peter;Klee,Victor;譚必信;Tam, Bit-shun
    贡献者: 淡江大學數學學系
    日期: 1995-07
    上传时间: 2010-01-28 07:26:31 (UTC+8)
    出版者: Elsevier
    摘要: For a closed, pointed n-dimensional convex cone K in Rn, let π(K) denote the set of all n × n real matrices A which as linear operators map K into itself. Let ∑(K) denote the set of all n × n matrices that are cross-positive on K, and L(K) = ∑(K) ∩ [− ∑(K)], the lineality space of ∑(K). Let Λ = RI, the set of all real multiples of the n × n identity matrix I. Then
    The final equality was proved in 1970 by Schneider and Vidyasagar, who showed also that π(K) + Λ = ∑(K) when K is polyhedral but not when K is a three-dimensional circular cone. They asked for a general characterization of those K for which the equality holds. It is shown here that if n ⩾ 3 and the cone K is strictly convex or smooth, then π(K) + Λ ≠ ∑(K); hence for n ⩾ 3 the equality fails for “almost all” K in the sense of Baire category. However, the equality does hold for some nonpolyhedral K, as was shown by a construction that appeared in the third author's 1977 dissertation and is explained here in more detail. In 1994 it was shown by Stern and Wolkowicz that the weaker equality π(K) + L(K) = ∑(K) holds for all ellipsoidal (as well as for all polyhedral) K, and they wondered whether this equality holds for all K. However, their equality certainly fails for all strictly convex or smooth K such that L(K) = Λ, and it is shown here that this also includes “almost all” K when n ⩾ 3.
    關聯: Linear Algebra and Its Applications 223-224, pp.285-305
    DOI: 10.1016/0024-3795(93)00364-6
    显示于类别:[數學學系暨研究所] 期刊論文


    档案 描述 大小格式浏览次数
    Cross-positive matrices revisted.pdf921KbAdobe PDF0检视/开启



    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library & TKU Library IR teams. Copyright ©   - 回馈