立方非负的不可约符号模式(英文)

Irreducible Sign Patterns With Nonnegative Cubes

以+,-,0为元素的矩阵称为符号模式矩阵。本文考虑符号模式矩阵的立方模式,给出了至少含一个负元的不可约符号模式的立方模式是非负的充要条件及在置换相似下的标准型;得到了立方非负的符号模式矩阵中出现的正元素的个数的最大(小)值及给出了达到这些最大(小)值的不可约符号模式矩阵的完整刻画。

A matrix whose entries are +,-, and 0 is called a sign pattern matrix. In this paper, we characterize the irreducible sign patterns with at least one negative entry, whose cube is nonnegative, and determine the maximum (respectively, minimum) number of positive entries that can occur in the cube of a irreducible sign pattern matrix A that contains at least one negative entry, whenever A3 > 0. Further we identify the irreducible sign patterns that achieve this maximum (respectively, minimum) number.