| 泛正定矩阵的进一步研究 |
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| 引用本文： | 杨虎,邵华. 泛正定矩阵的进一步研究[J]. 数学的实践与认识, 2008, 38(3): 114-122 |
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| 作者姓名： | 杨虎 邵华 |
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| 作者单位： | 重庆大学,数理学院,重庆,400030 |
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| 摘 要： | 给出了泛正定矩阵的重要性质与充要条件.进而提出了新的泛正定与泛非负定矩阵子集类的定义.在其基础上给出泛正定子集类的一系列性质,尤其是推广了Minkowski不等式.最后讨论了泛非负定子集类上的一种新的矩阵偏序的性质与充要条件.
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| 关 键 词： | 泛正定矩阵 Minkowski不等式 偏序 |
| 修稿时间： | 2006-10-13 |
A Further Study on Universal Positive Definite Matrices |
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| YANG Hu,SHAO Hua. A Further Study on Universal Positive Definite Matrices[J]. Mathematics in Practice and Theory, 2008, 38(3): 114-122 |
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| Authors: | YANG Hu SHAO Hua |
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| Abstract: | For judging the universal positive definite matrices in literature,some necessary and sufficient conditions are given as well as some significant useful properties.Further,two special subsets in universal positive definite matrices and universal nonnegative definite matrices are introduced,and some further properties of the former are discussed,especially the well-known Minkowski inequality of two matrices.Finally,a new partial ordering in the subset of universal nonnegative definite matrices is defined and some properties and conditions for their existence are discussed. |
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| Keywords: | universal positive definite matrix Minkowski inequality partial ordering |
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