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矩阵空间上保弱伴随矩阵的线性映射
引用本文:张平.矩阵空间上保弱伴随矩阵的线性映射[J].纯粹数学与应用数学,2009,25(3):573-578.
作者姓名:张平
作者单位:三峡大学理学院,湖北,宜昌,443002 
基金项目:湖北省教育厅重点科研项目,三峡大学科学基金 
摘    要:为了刻画矩阵空间上保弱伴随矩阵的线性映射f,引入了保弱伴随矩阵的概念,以矩阵的弱伴随矩阵为不变量,得到了当n≥3时数域F上从线性矩阵空间Mn×n(F)到Mm×m(F)的保弱伴随矩阵的线性映射f的形式.

关 键 词:线性保持问题  单射  伴随矩阵  弱伴随矩阵  

Linear operators preserving weak adjoint matrix between matrix spaces
ZHANG Ping.Linear operators preserving weak adjoint matrix between matrix spaces[J].Pure and Applied Mathematics,2009,25(3):573-578.
Authors:ZHANG Ping
Institution:ZHANG Ping ( College of Science,China Three Gorges University,Yichang 443002,China)
Abstract:In this paper, in order to characterize the linear operators on matrix spaces that preserve weak adjoint matrix, we introduce the definition of the preserving weak adjoint matrix and make use of the weak adjoint matrix as the invariant, and then obtain the form of the linear operators from the linear space of Mn×n(F) into Mm×m(F) over the number field F that preserve weak adjoint matrix, where n ≥ 3.
Keywords:linear preserver problem  injective map  adjoint matrix  weak adjoint matrix  rank  
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