jsp.display-item.identifier=請使用永久網址來引用或連結此文件:
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/58749
|
| 题名: | Maximal exponents of polyhedral cones (I) |
| 作者: | Loewy, Raphael;Tam, Bit-Shun |
| 贡献者: | 淡江大學數學學系 |
| 关键词: | Cone-preserving map;K-primitive matrix;Exponents;Polyhedral cone |
| 日期: | 2010-05 |
| 上传时间: | 2011-10-01 21:08:22 (UTC+8) |
| 出版者: | Maryland Heights: Academic Press |
| 摘要: | Let K be a proper (i.e., closed, pointed, full convex) cone in Rn. An n×n matrix A is said to be K-primitive if there exists a positive integer k such that Ak(K\{0}) ⊆ int K; the least such k is referred to as the exponent of A and is denoted by γ(A). For a polyhedral cone K, the maximum value of γ(A), taken over all K-primitive matrices A, is called the exponent of K and is denoted by γ(K). It is proved that if K is an n-dimensional polyhedral cone with m extreme rays then for any K-primitive matrix A, γ(A) ≦ (mA − 1)(m − 1) + 1, where mA denotes the degree of the minimal polynomial of A, and the equality holds only if the digraph (E,P(A,K)) associated with A (as a cone-preserving map) is equal to the unique (up to isomorphism) usual digraph associated with an m x m primitive matrix whose exponent attains Wielandt’s classical sharp bound. As a consequence, for any n-dimensional polyhedral cone K with m extreme rays, γ(K) ≦ (n−1)(m−1)+1. Our work answers in the affirmative a conjecture posed by Steve Kirkland about an upper bound of γ(K) for a polyhedral cone K with a given number of extreme rays. |
| 關聯: | Journal of Mathematical Analysis and Applications 365(2), pp.570-583 |
| DOI: | 10.1016/j.jmaa.2009.11.016 |
| 显示于类别: | [應用數學與數據科學學系] 期刊論文
|
文件中的档案:
| 档案 |
描述 |
大小 | 格式 | 浏览次数 |
|---|
| 0022-247X_365(2)p570-583.pdf | | 337Kb | Adobe PDF | 293 | 检视/开启 | | 0022-247X_365(2)p570-583.pdf | | 337Kb | Adobe PDF | 2 | 检视/开启 |
|
在機構典藏中所有的数据项都受到原著作权保护.
|