| 矩阵的酉不变范数不等式 |
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| 引用本文： | 任林源,张利军.矩阵的酉不变范数不等式[J].数学的实践与认识,2011,41(11). |
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| 作者姓名： | 任林源 张利军 |
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| 作者单位： | 1. 西安工业大学数理系,陕西西安,710032
2. 哈尔滨工程大学自动化学院,黑龙江哈尔滨,150001 |
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| 基金项目： | 陕西省教育厅科研计划资助项目，校长科研基金项目 |
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| 摘 要： | 利用凹函数和半正定矩阵的性质,讨论并且得到了一些矩阵Rotfel型范数不等式.另外,通过研究Hermitian矩阵和斜Hermitian矩阵和的特征值的模行列式的不等式,得到一些关于Hermitian矩阵和斜Hermitian矩阵和的范数不等式.推广了文献中的相关结果.
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| 关 键 词： | 酉不变范数 凹函数 半正定矩阵 Hermitian矩阵 斜Hermitian矩阵 |
The Matrix Inequalities for Unitarily Invariant Norms |
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| REN Lin-yuan,ZHANG Li-jun.The Matrix Inequalities for Unitarily Invariant Norms[J].Mathematics in Practice and Theory,2011,41(11). |
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| Authors: | REN Lin-yuan ZHANG Li-jun |
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| Abstract: | With the character of concave function and semi-positive definite matrices,some new results of norm inequality related to Rotfel's,trace inequality for some concave functions and arbitrary matrix were given.In addition,through studying the Hermitian matrix and skew Hermitian matrix and the characteristic value of the mode of the determinant inequality are Hermitian matrix and get some about the Hermitian matrix and unitarily invariant norms. The paper generalizes the result in the literature. |
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| Keywords: | Unitarily invariant norms concave function semi-positive definite matrix Hermitian matrix skew Hermitian matrix |
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