| Quantale矩阵的广义逆及其正定性 |
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| 引用本文： | 梁少辉,赵彬.Quantale矩阵的广义逆及其正定性[J].模糊系统与数学,2009,23(5). |
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| 作者姓名： | 梁少辉 赵彬 |
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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 |
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| 摘 要： | 给出Quantale矩阵{1}-广义逆的一种刻划以及存在的条件,给出Quantale矩阵M-P广义逆的定义,讨论Quantale矩阵M-P广义逆的若干性质,得到Quantale矩阵M-P广义逆的具体形式.引入Quantale矩阵正定性的概念,研究交换幂等Quantale上矩阵正定的一些性质,得到交换幂等Quantale上矩阵正定的一些等价刻画.
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| 关 键 词： | Quantale矩阵 {1}-广义逆 M-P广义逆 正定性 |
Generalized Inverse of Quantale Matrixs and Its Positive Definiteness |
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| Abstract: | Firstly, some characteristics of generalized {1}-inverse of quantale matrixs are given, and the generalized {l}-inverse of quantale matrixs exists when some conditions are satisfied. Secondly, the definition of generalized M-P inverse of quantale matrixs is given. Some properties of generalized M-P inverse of quantale matrixs are studied. Meanwhile, we give the structure of generalized M-P inverse of quantale matrixs. At last, the definition of positive definiteness of quantale matrixs introduced, some properties of positive definiteness of quantale matrixs are discussed. And some characteristics for a quantale matrixs to be positive definiteness are obtained. |
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| Keywords: | Quantale Matrix Generalized {l}-inverse Generalized M-P Inverse Positive Definiteness |
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