对称符号模式矩阵的幂等性质及结构

The idempotent properties and structure of symmetric sign pattern matrices

将F.J.Hall,李忠善和B.Rao及Hall[Lin.Alg.Appl.2004.393:233-251],[Lin.Agl.Appl.1994.211:53-66]对于非负符号模式矩阵的结果推广到了对称符号模式矩阵.给出了对称符号模式矩阵的允许幂等与符号幂等的关系,确定出对称符号模式矩阵的广义置换相似结构和最小秩结构,得出了对称符号模式矩阵的广义逆及其幂等之间的关系.

By extending the results for nonnegative sign patterns in Hall,Li and Rao [Lin.Agl.Appl,2004.393： 233-251],Eschenbach,Hall and Li [Lin.Agl.Appl,1994.211： 53-66],the relation between sign idempotent and allowance of idempotent is given in symmetric sign pattern matrices.At the same time,the generalized permutationally similar idempotent structure and minimum rank factorization are obtained.Finally,the relation between generalized inverses and idempotent is researched.