| 次Hermite矩阵的次正定性 |
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| 引用本文： | 曹莉莉.次Hermite矩阵的次正定性[J].西南师范大学学报(自然科学版),1996(3). |
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| 作者姓名： | 曹莉莉 |
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| 作者单位： | 重庆商学院 |
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| 摘 要： | 若ｎ阶次Ｈｅｒｍｉｔｅ矩阵Ａ，对任意非零向量Ｘ＇＝（ｘ＿１，ｘ＿２，…ｘ＿ｎ）∈Ｒ￣ｎ，有ＡＸ＞０，则称次Ｈｅｒｍｉｔｅ矩阵Ａ是次正定的．给出了判定次Ｈｅｒｍｉｔｅ矩阵次正定的几个充要条件：定理ｎ阶次Ｈｅｒｍｉｔｅ矩阵Ａ是次正定的，当且仅当下列条件之一成立：（ｌ）Ｈｅｒｍｉｔｅ矩阵ＪＡ是正定的；（２）存在ｎ阶可逆复矩阵Ｐ，使ＡＰ＝Ｊ；（３）次Ｈｅｒｍｉｔｅ矩阵Ａ的４ｋ阶，４ｋ十互阶下次主子式为正，４ｋ＋２阶，４ｋ＋３阶下次主子式为负；（４）存在ｎ阶可逆复矩阵Ｐ，使其中λ＿ｉ＞０，ｉ＝１，２，…，ｎ。
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| 关 键 词： | 次对称矩阵 次Hermite矩阵 次正定次Hermite矩阵 |
The metapositive definiteness of sub-Hermite matrix |
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| Cao lili.The metapositive definiteness of sub-Hermite matrix[J].Journal of Southwest China Normal University(Natural Science),1996(3). |
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| Authors: | Cao lili |
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| Abstract: | In u-space, for then sub-Hermite matrix A= (aij) is metapositive definiteness.The metaposihve definiteness of sub-Hermite matrix are given.If sub-Hcrmite matrix A is metapositive definiteness, if and only 1) Hermits matrix JA is positively definite matrix;2) exist inverse complex matrix P, such as 3) its lower sub-main subdeterminant is positive when K=4k, 4k 1; A is negative when K =4k 2, 4k 3 ;4) exist inverse complex matrix P, such as |
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| Keywords: | sub-Hermite matrix metapositive definiteness sub-Hermite matrix sub-symmetric matrix |
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