反中心自共轭矩阵的一些性质

段淑娟; 秦建国

doi:10.3969/j.issn.2096-1553.2017.6.014

November 2017

Article Contents

DUAN Shu-juan and QIN Jian-guo. Properties on centroskew self-conjugate matrix[J]. Journal of Light Industry, 2017, 32(6): 105-108. doi: 10.3969/j.issn.2096-1553.2017.6.014

Citation: DUAN Shu-juan and QIN Jian-guo. Properties on centroskew self-conjugate matrix[J]. Journal of Light Industry, 2017, 32(6): 105-108. doi: 10.3969/j.issn.2096-1553.2017.6.014 shu

Properties on centroskew self-conjugate matrix

College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China

Received Date: 2016-09-15
Available Online: 2017-11-15

Abstract

The definition of centroskew self-conjugate matrix and some matrix theories were introduced.It was proved that the transposed matrix A^T,and inversion A^-1(A≠0) of a centroskew self-conjugate matrix A were still centroskew self-conjugate matrix. The direct product of any two centroskew self-conjugate matrix was centroskew self-conjugate matrix. The A^* of an even order centroskew self-conjugate matrix and A^m of the odd number degree power were still centroskew self-conjugate matrix. When the centroskew self-conjugate matrix of A and -A had the same characteristic values, and 0≠X₀=(a₁,a₂,…,a_n)^T∈Cⁿ was a characteristic vector of the characteristic value λ₀ belonging to a centroskew self-conjugate matrix A∈C^n×n, VX₀=(a_n,a_n-1,…,a₁)^T was also a characteristic vector of the characteristic value λ₀ belonging to -A.
- centroskew self-conjugate matrix,
- flip matrix,
- adjoint matrix,
- inverse matrix
References
1. [1]
  袁晖坪.次亚正定矩阵[J].数学杂志,2001,21(1):29.
2. [2]
  QIN J G,SONG G A.The general and centro(skew) symmetric solutions to a system of matrix equations over an arbitrary skew field[J].Chin Quart J of Math,2006,21(1):66.
3. [3]
  周永安,秦韬.关于中心对称矩阵的几个性质[J].数学的实践与认识,2008(8):186.
4. [4]
  谭瑞梅,薛雪莉.关于反中心对称矩阵的某些性质探讨[J].大学数学,2010,26(4):173.
5. [5]
  程云鹏,张凯院,徐仲.矩阵论[M].西安:西北工业大学出版社,2006.
6. [6]
  陈公宁.矩阵理论与应用[M].北京:科学出版社,2007.
Proportional views

Get Citation

PDF

XML

Article Metrics

Article views(1228) PDF downloads(26) Cited by()

Ralated

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Properties on centroskew self-conjugate matrix

Abstract

References

Proportional views

Article Metrics

Ralated

Proportional views

通讯作者: 陈斌, bchen63@163.com