期刊論文
| 學年 | 98 |
|---|---|
| 學期 | 2 |
| 出版（發表）日期 | 2010-05-01 |
| 作品名稱 | Maximal exponents of polyhedral cones (I) |
| 作品名稱（其他語言） | |
| 著者 | Loewy, Raphael; Tam, Bit-Shun |
| 單位 | 淡江大學數學學系 |
| 出版者 | Maryland Heights: Academic Press |
| 著錄名稱、卷期、頁數 | Journal of Mathematical Analysis and Applications 365(2), pp.570-583 |
| 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. |
| 關鍵字 | Cone-preserving map; K-primitive matrix; Exponents; Polyhedral cone |
| 語言 | en |
| ISSN | 0022-247X |
| 期刊性質 | 國外 |
| 收錄於 | SCI |
| 產學合作 | |
| 通訊作者 | Tam, Bit-Shun |
| 審稿制度 | 是 |
| 國別 | USA |
| 公開徵稿 | |
| 出版型式 | 紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/58749 ) |