| 矩阵的保半正定性 |
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| 引用本文： | 秦晓燕,任芳国.矩阵的保半正定性[J].纺织高校基础科学学报,2011,24(3):403-405. |
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| 作者姓名： | 秦晓燕 任芳国 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安,710062 |
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| 基金项目： | 国家自然科学基金资助项目，陕西师范大学重点基金资助项目 |
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| 摘 要： | 利用经典的半正定Hermite矩阵的等价条件,讨论了2×2分块矩阵的保半正定性问题.A为2×2半正定Hermite分块矩阵时,则对每一子块分别取迹、行列式、谱范数、秩、数值域后所成矩阵仍为半正定；当A为2×2分块矩阵时,(A)的范数和数值域半径分别不超过(A)的范数和数值域半径.
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| 关 键 词： | 半正定矩阵 压缩矩阵 谱范数 |
The preserver problems of positive semidefinite matrix |
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| QN Xiao-yan,REN Fang-guo.The preserver problems of positive semidefinite matrix[J].Basic Sciences Journal of Textile Universities,2011,24(3):403-405. |
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| Authors: | QN Xiao-yan REN Fang-guo |
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| Affiliation: | Q1N Xiao-yan,REN Fang-guo |
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| Abstract: | By using the classical conditions of equivalence of semidefinite Hermite block matrix sufficiently,the problem of maintaining semidefiniteness with two by two block matrix are mainly discussed.Firstly,if A∈Mn is a positive semidefinite Hermite block matrix,the resulting matrix that is taken trace,determinant,spectrum norm,rank and numerical radius for every block matrix respectively is still positive semidefinite.Secondly,if A∈Mn is a block matrix,the norm and numerical radius of A are not exceeded that of . |
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| Keywords: | semidefinite matrix contraction matrix spectrum norm |
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