非负不可约模式的最小秩(英文)

The Minimum Rank of Nonnegative Irreducible Patterns

设A是n阶非负不可约模式.A的最小秩定义为与A有相同符号模式的全体实矩阵的秩的最小值.考虑矩阵序列A,A2,…,A3,….设Ab是第一个重复的矩阵,且记p>0是最小的正整数使得Ab=Ab+p.称b为A的基.p为A的周期.本文研究了非负不可约模式的基与最小秩的关系.

Let A be an n × n nonnegative irreducible pattern. The minimum rank of A is the minimum of ranks of all real matrices which have the same sign pattern as A. Consider the sequence A, A2, A3, [midline ellipsis] . Let Ab be the first one that is repeated. Write Ab = Ab+p with p>0 minimal. Then b is called the base of A, and p the period of A. We study the relations between the base and the minimum rank of nonnegative irreducible pattern A.