| 关于半正定矩阵迹的几何—算术平均不等式 |
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| 引用本文： | 刘建华.关于半正定矩阵迹的几何—算术平均不等式[J].重庆大学学报(自然科学版),1989(5). |
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| 作者姓名： | 刘建华 |
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| 作者单位： | 重庆大学应用数学系 |
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| 摘 要： | 本文首先证明了关于Hermite矩阵迹的一个不等式,在此基础上,得出了关于半正定矩阵迹的几何-算术平均不等式,特别地,该不等式对实对称半正定阵也是成立的,这就给出了文〔1〕中,R.Bellman所提问题的一个回答。
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| 关 键 词： | Hermite矩阵 对称矩阵 半正定矩阵 迹 不等式 |
THE GEOMETRIC-ARITHMETRIC-MEAN INEQUALITY FOR POSITIVE SEMIDEFINITE MATRIX TRACES |
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| Liu Jianhua.THE GEOMETRIC-ARITHMETRIC-MEAN INEQUALITY FOR POSITIVE SEMIDEFINITE MATRIX TRACES[J].Journal of Chongqing University(Natural Science Edition),1989(5). |
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| Authors: | Liu Jianhua |
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| Institution: | Liu Jianhua |
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| Abstract: | In this paper, we firstly prove an inequality for Hermite matrix traces, then present an -inequality for positive semidefinite Hermite matrix traces. Particularly it holds for real symmetric positive semidefinite matrix traces, thus giving an answer to an open question proposed by R.Bellman. |
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| Keywords: | Hermite matrix symmetric matrix positive semidefinite matrix trace inequelity |
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