| 对称部分为半正定的方阵 |
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| 引用本文： | 李炯生.对称部分为半正定的方阵[J].数学学报,1996,39(3):376-381. |
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| 作者姓名： | 李炯生 |
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| 作者单位： | 中国科学技术大学数学系 |
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| 摘 要： | 所有ｎ阶具有半正定对称部分的方阵的集合记作ＰＳＤｎ．本文给出了ＰＳＤｎ中方阵在合同下的标准形以及ＰＳＤｎ中两个方阵合同的一个充要条件，并给出了ＰＳＤｎ中一个方阵及其对称部分与斜对称部分的主子式间的一个不等式．
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| 关 键 词： | 对称部分为半正定的方阵，合同，标准形，主子式 |
| 收稿时间： | 1994-7-1 |
| 修稿时间： | 1994-12-19 |
Matrices Whose Symmetric Part is Positive Semidefinite |
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| Li Jiongsheng.Matrices Whose Symmetric Part is Positive Semidefinite[J].Acta Mathematica Sinica,1996,39(3):376-381. |
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| Authors: | Li Jiongsheng |
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| Institution: | Li Jiongsheng(Department of Mathematics, University of Science and Techonology of China, Hefei 230026, China) |
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| Abstract: | The set of all real n-by--n matrices whose symmetric part is positive semidefinite is denoted by PSDn. In this paper, we give the canonical form of a matrix in PSDn under congruence and a necessary and sufficient condition for two matrices in PSDn to be congruent.Moreover we give an inequality concerning the determinant of a matrix in PSDn and those of its symmetric and skew symmetric parts. |
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| Keywords: | matrix whose symmetric part is positive semidefinite congruence canonical form principal minor |
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