| 正定矩阵性质的推广 |
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| 引用本文： | 刘畅,徐兆棣.正定矩阵性质的推广[J].沈阳师范大学学报(自然科学版),2009,27(3):267-271. |
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| 作者姓名： | 刘畅 徐兆棣 |
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| 作者单位： | 沈阳师范大学数学与系统科学学院,辽宁沈阳,110034 |
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| 基金项目： | 辽宁省自然科学基金资助项目 |
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| 摘 要： | 通过运用正定矩阵的定义和一般理论,得出了正定(半正定)矩阵的偏序理论,即A-B是正定(半正定)矩阵的一些重要性质,得出了一些矩阵不等式;并将代数中的均值不等式推广到矩阵形式的不等式,并将其推广.文中有的定理证明从不同的角度,给出了不同的证明方法.
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| 关 键 词： | 矩阵 正定 半正定 偏序 不等式 |
Further Extension of Properties in Positive Matrices |
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| LIU Chang,XU Zhao-di.Further Extension of Properties in Positive Matrices[J].Journal of Shenyang Normal University: Nat Sci Ed,2009,27(3):267-271. |
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| Authors: | LIU Chang XU Zhao-di |
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| Abstract: | According to the definition and general theories of positive semi-definited matrices, we introduce the theory of partial ordering in positive definited (positive semi-definited) matrices, that is positive definited (positive semi-definite) matrices;We discuss some important properties which we called matrix inequalities, and put the average value inequalities extended on the matrices. Different approach had been taken from different points of view in some theorems. |
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| Keywords: | matrice positive definited positive semi-definited partial ordering inequalities |
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