摘要
利用经典的Cayley-Hamilton定理,给出了矩阵core-EP逆和DMP逆的多项式方程.设奇异矩阵A的特征多项式为p_A(s)=det(_sE_n-A)=s^n+a_(n-1)s_(n-1)+…+a_1s,则f_A(A~⊕)=0和f_A(A^(d,+))=0,其中f_A(A)=a_1x^n+a_2x^(n-1)+…+a_(n-1)x^2+x,A~⊕和A^(d,+)分别是A的core-EP逆和DMP逆.并进一步讨论了A^D∈C_(n,n)和A~⊕∈C_(n,n)的特征多项式的性质.
By using the classical Cayley-Hamilton theorem,the polynomial equations of the core-EP inverse matrix and Drazin-Moore-Penrose(DMP)inverse matrix are given,respectively.If the characteristic polynomial of the singular matrix A,p A(s)=det(s E n-A)=s n+a n-1 s n-1+…+a 1 s,is given,then f A(A)=0 and f A(A d,+)=0 in which f A(A)=a 1 x n+a 2 x n-1+…+a n-1 x 2+x,and A and A d,+are the core-EP inverse and the DMP inverse of A,respectively.Furthermore,some properties of the characteristic polynomials of A D∈C n,n and A∈C n,n are derived.
作者
王宏兴
陈建龙
闫观捷
Wang Hongxing;Chen Jianlong;Yan Guanjie(School of Mathematics,Southeast University,Nanjing 211189,China;School of Science,Guangxi University for Nationalities,Nanning 530006,China)
基金
The China Postdoctoral Science Foundation(No.2015M581690)
the National Natural Science Foundation of China(No.11371089)
the Natural Science Foundation of Jiangsu Province(No.BK20141327)
the Special Fund for Bagui Scholars of Guangxi