|Table of Contents|

[1] Wang Hongxing, Chen Jianlong, Yan Guanjie, et al. Generalized Cayley-Hamilton theoremfor core-EP inverse matrix and DMP inverse matrix [J]. Journal of Southeast University (English Edition), 2018, 34 (1): 135-138. [doi:10.3969/j.issn.1003-7985.2018.01.019]
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Generalized Cayley-Hamilton theoremfor core-EP inverse matrix and DMP inverse matrix()
矩阵core-EP逆和DMP逆的广义Cayley-Hamilton定理

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
34
Issue:
2018 1
Page:
135-138
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2018-03-20

Info

Title:
Generalized Cayley-Hamilton theoremfor core-EP inverse matrix and DMP inverse matrix
矩阵core-EP逆和DMP逆的广义Cayley-Hamilton定理
Author(s):
Wang Hongxing1, 2, Chen Jianlong1, Yan Guanjie2
1School of Mathematics, Southeast University, Nanjing 211189, China
2School of Science, Guangxi University for Nationalities, Nanning 530006, China
王宏兴1, 2, 陈建龙1, 闫观捷2
1东南大学数学学院, 南京 211189; 2广西民族大学理学院, 南宁 530006
Keywords:
Cayley-Hamilton theorem;  characteristic equation;  Drazin inverse;  Drazin-Moore-Penrose(DMP)inverse;  core-EP inverse
Cayley-Hamilton定理;  特征方程;  Drazin逆;  DMP逆;  core-EP逆
PACS:
O151.2
DOI:
10.3969/j.issn.1003-7985.2018.01.019
Abstract:
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, pA(s)=det(sEnn-A)=sn+an-1sn-1+…+a1s, is given, then fA(A⊕)=0 and fA(Ad, +)=0 in which fA(A)=a1xnn+a2xn-1+…+an-1x2+x, and A⊕ and Ad, + are the core-EP inverse and the DMP inverse of A, respectively. Furthermore, some properties of the characteristic polynomials of AD∈Cn, n and A⊕∈Cn, n are derived.
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pA(s)=det(sEnn-A)=sn+an-1sn-1+…+a1s, 则fA(A⊕)=0和fA(Ad, +)=0, 其中fA(A)=a1xnn+a2xn-1+…+an-1x2+x, A⊕和Ad, +分别是A的core-EP逆和DMP逆.并进一步讨论了AD∈Cn, n和A⊕∈Cn, n的特征多项式的性质.

References:

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Memo

Memo:
Biographies: Wang Hongxing(1981—), male, doctor; Chen Jianlong(corresponding author), male, doctor, professor, 101004157@seu.edu.cn.
Foundation items: 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.
Citation: Wang Hongxing, Chen Jianlong, Yan Guanjie. Generalized Cayley-Hamilton theorem for core-EP inverse matrix and DMP inverse matrix[J].Journal of Southeast University(English Edition), 2018, 34(1):135-138.DOI:10.3969/j.issn.1003-7985.2018.01.019.
Last Update: 2018-03-20