| 有关矩阵广义逆$A^{(2)}_{T,S}$的惯性指数及其应用 |
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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),1959,46(4):395-398. |
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| 作者姓名： | 吴中成 贺宁馨 |
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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。
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| 关 键 词： | 惯性指数 广义逆 正定(半正定） 负定(半负定） |
Inertia formulae related to the generalized inverse $A^{(2)}_{T,S}$ with applications |
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| WU Zhongcheng,HE Ningxin.Inertia formulae related to the generalized inverse $A^{(2)}_{T,S}$ with applications[J].Journal of Zhejiang University(Sciences Edition),1959,46(4):395-398. |
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| Authors: | WU Zhongcheng HE Ningxin |
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| Institution: | 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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| 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. |
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| Keywords: | inertia generalized inverse positive (semi-)definite negative(semi-)definite |
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