论文标题:环上矩阵的加权Moore-Penrose逆
Weighted Moore-Penrose Inverse of Matrices Over Rings
论文作者
论文导师 罗彦锋,论文学位 硕士,论文专业 基础数学
论文单位 兰州大学,点击次数 113,论文页数 33页File Size1038k
2006-04-01论文网 http://www.lw23.com/lunwen_181662347/
weighted Moore-Penrose inverse;Moore-Penrose inverse;unimodule matrix;semiring.
加权Moore-Penrose逆是一种特殊的广义逆,它不仅是许多数学分支的基本工具,而且在经济学、信息处理、自动控制等其他领域有着广泛的应用,近年来,结合环、半环等更一般的代数系统的矩阵广义逆的研究,不仅将广义逆的理论和方法作了更加深入的推广,而且也成了刻画代数结构的有力工具。 本文给出一般含幺环上矩阵加权Moore-Penrose逆存在的充要条件,并将其推广到一般半环上。另外,在矩阵具有加权Moore-Penrose逆的基础上,讨论了交换含幺环上它的加权Moore-Penrose逆与加边矩阵的关系,并给出加权Moore-Penrose逆的行列式表示。
The weighted Moore-Penrose inverse is a special generalized inverse which is an important basic tool in many branches of mathematics and has extensive applications in other fields such as economics, information processing, automatic control, etc. Recently, the study of generalized inverse of matrices associating with more general algebra such as ring, semiring and so on generalize the theory and methods of generalized inverse deeply and characterize the structure of algebra as well.In this paper, we"ll give a necessary and sufficient condition for the existence of the weighted Moore-Penrose inverse of a matrix over a ring and generalize it on a semiring. In addition, we"ll discuss the relationship between the weighted Moore-Penrose inverse of a matrix and its bording and give the determinantal expression of the weighted Moore-Penrose inverse.
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