On the Zn sign pattern matrices

Journal of Shanghai Normal University (Natural Sciences)

ZHANG Jizhou¹  FANG Maozhong² 

[1] College of Mathematics and Sciences,Shanghai Normal University;School of Mathematics and Information,Shanghai Lixin University of Commerce;

关键词: sign pattern matrix;    closure;    reducible;   

DOI  :  

来源: DOAJ

【 摘 要 】

Let Z_n dente the set of all square sign pattern matrices of order n whose off-diagonal entries are non-positive.For a sign pattern matrix A∈Z_n and two arbitrary real matrices B₁,B₂ with sign pattern A,if sgn(B₁B₂)∈Z_n,then we call this property the closure property of Z_n.We prove that if A∈Z_n(n≥3) and A has the closure property of Z_n,then A must be reducible.We also characterize this kind of Z_n sign pattern matrices.

【 授权许可】

Unknown