Quantale矩阵的广义逆及其正定性  

Generalized Inverse of Quantale Matrixs and Its Positive Definiteness

作　　者：梁少辉[1] 赵彬[1] LIANG Shao—hui;ZHAO Bin(College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2009年第5期41-47,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10871121)

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。Firstly,some characteristics of generalized{1}-inverse of quantale matrixs are given,and the generalized{1}-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.

关 键 词：QUANTALE矩阵 {1}-广义逆 M-P广义逆 正定性 

分 类 号：O153[理学—数学]