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[1] Wang Long, Chen Jianlong,. A note on the Moore-Penrose inverse of a companion matrix [J]. Journal of Southeast University (English Edition), 2017, 33 (1): 123-126. [doi:10.3969/j.issn.1003-7985.2017.01.020]
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A note on the Moore-Penrose inverse of a companion matrix()
关于友矩阵的Moore-Penrose逆的一个注记
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
33
Issue:
2017 1
Page:
123-126
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2017-03-30

Info

Title:
A note on the Moore-Penrose inverse of a companion matrix
关于友矩阵的Moore-Penrose逆的一个注记
Author(s):
Wang Long,Chen Jianlong
Department of Mathematics, Southeast University, Nanjing 211189, China
王龙,陈建龙
东南大学数学系, 南京 211189
Keywords:
companion matrix;  Moore-Penrose inverse;  ring
友矩阵;  Moore-Penrose 逆;  环
PACS:
O151.2
DOI:
10.3969/j.issn.1003-7985.2017.01.020
Abstract:
Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices over R is investigated and the sufficient and necessary conditions for such existence are obtained. Furthermore, the representation of the Moore-Penrose inverse of M=［0 AC B］ is given under the condition of EBF=0, where E=I-CC† and F=I-A†A. This result generalizes the representation of the Moore-Penrose inverse of the companion matrix M=［0 aInn b］ due to Pedro Patrício. As for applications, some examples are given to illustrate the obtained results.
假设R是一个有单位元1的结合环.探讨了R上分块矩阵Moore-Penrose逆的存在性,得到了环上分块矩阵的Moore-Penrose逆存在性的充要条件.进而,在EBF=0条件下,其中E=I-CC†和F=I-A†A,给出了Moore-Penrose逆的表达式M=［0 AC B］.此结果推广了Pedro Patrício 关于友矩阵M=［0 aInn b］的Moore-Penrose逆表达式.作为应用,给出一些例子验证了所得到的结果.

References:

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Memo

Memo:
Biographies: Wang Long(1988—), male, graduate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen @seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371089), the Natural Science Foundation of Jiangsu Province(No.BK20141327), Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020), the Natural Science Foundation of Jiangsu Higher Education Institutions of China(No.15KJB110021).
Citation: Wang Long, Chen Jianlong. A note on the Moore-Penrose inverse of a companion matrix[J].Journal of Southeast University(English Edition),2017,33(1):123-126.DOI:10.3969/j.issn.1003-7985.2017.01.020.
Last Update: 2017-03-20