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 题名: Maximal exponents of polyhedral cones (II) 作者: Raphael Loewy;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;Exp-maximal cone;Exp-maximal K-primitive matrix;Cone-equivalence;Minimal cone 日期: 2010-06-01 上传时间: 2011-10-01 21:08:26 (UTC+8) 出版者: Philadelphia: Elsevier Inc. 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 ; 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 the maximum value of γ(K) as K runs through all n-dimensional minimal cones (i.e., cones having n+1 extreme rays) is n2-n+1 if n is odd, and is n2-n if n is even, the maximum value of the exponent being attained by a minimal cone with a balanced relation for its extreme vectors. The K-primitive matrices A such that γ(A) attain the maximum value are identified up to cone-equivalence modulo positive scalar multiplication. 關聯: Linear Algebra and its Applications 432(11), pp.2861-2878 DOI: 10.1016/j.laa.2009.12.026 显示于类别: [數學學系暨研究所] 期刊論文