k次幂非正的符号模式矩阵

本首先对使得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A^2≤0的符号模式矩阵A的充分必要条件。

On the Sign Pattern Matrices with Nonpositive k-power

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 Ak ≤ 0.Further, we determine the maximum number of negative entries that can occur in A whenever Ak ≤ 0. Finally, we give a necessity and sufficiency condition for A2 ≤ 0.