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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (4): 395-398    DOI: 10.3785/j.issn.1008-9497.2019.04.002
数学与计算机科学     
有关矩阵广义逆$A^{(2)}_{T, S}$的惯性指数及其应用
吴中成1, 贺宁馨2
1.上海工程技术大学 数理与统计学院，上海 201620
2.贵州师范大学 数学科学学院，贵州 贵阳 550001
Inertia formulae related to the generalized inverse $A^{(2)}_{T, S}$ with applications
WU Zhongcheng1, HE Ningxin2
1.School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
2.School of Mathematics Science, Guizhou Normal University, Guiyang 550001, China
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摘要： 建立了某些有关矩阵广义逆$A^{(2)}_{T, S}$表达式的惯性指数公式。基于所得惯性指数，作为应用研究了矩阵的正定(半正定）性、负定(半负定）性。 给出了一些矩阵分别为正定矩阵、半正定矩阵、负定矩阵、半负定矩阵的充分必要条件。
关键词： 惯性指数;  广义逆;  正定(半正定）;  负定(半负定）    
Abstract: In this paper,firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse $A^{(2)}_{T, S}$. Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices. Finally,necessary and sufficient conditions for some matrices to be positive definite, positive semi-definite, negative definite and negative semi-definite are given, respectively.
Key words: inertia    generalized inverse    positive (semi-)definite    negative(semi-)definite
出版日期: 2019-07-25
CLC:  O151.21  
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引用本文:

吴中成, 贺宁馨. 有关矩阵广义逆$A^{(2)}_{T, S}$的惯性指数及其应用[J]. 浙江大学学报（理学版）, 2019, 46(4): 395-398.

WU Zhongcheng, HE Ningxin. Inertia formulae related to the generalized inverse $A^{(2)}_{T, S}$ with applications. Journal of Zhejiang University (Science Edition), 2019, 46(4): 395-398.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.04.002    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I4/395

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