κ次幂非正的符号模式矩阵(英文)

On the Sign Pattern Matrices with Nonpositive κ-power

中文关键词:  符号模式  矩阵  有向图

英文关键词:sign pattern  matrix  digraph.

中文摘要:

      本文首先对使得A^k≤0的符号模式矩阵A进行了刻画(k为任意正整数),进而决定了这类矩阵中负元个数的最大值.最后给出了使得A²≤0的符号模式矩阵A的充分必要条件.

英文摘要:

      A matrix whose entries are +,-, and 0 is called a sign pattern matrix. Let k be arbitrary positive integer. We first characterize sign patterns A such that .A^k≤0. Further, we determine the maximum number of negative entries that can occur in A whenever A^k≤0. Finally, we give a necessity and sufficiency condition for A²≤0.