|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()
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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
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
Keywords:
Cayley-Hamilton theorem;  characteristic equation;  Drazin inverse;  Drazin-Moore-Penrose(DMP)inverse;  core-EP inverse
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.

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