# 關鍵字查詢 | 類別：期刊論文 | | 關鍵字：Cross-positive matrices revisted

[第一頁][上頁]1[次頁][最末頁]目前在第 1 頁 / 共有 01 筆查詢結果

1 83/2 數學系 譚必信 教授 期刊論文 發佈 Cross-positive matrices revisted , [83-2] ：Cross-positive matrices revisted期刊論文Cross-positive matrices revistedGritzmann, Peter; Klee,Victor; 譚必信; Tam, Bit-shun淡江大學數學學系ElsevierLinear Algebra and Its Applications 223-224, pp.285-305For 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 π(K)+Δ⊆π(K)+L(K)⊆cl[π(K)+Δ]=Σ(K). 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
[第一頁][上頁]1[次頁][最末頁]目前在第 1 頁 / 共有 01 筆查詢結果