Invertible linear maps preserving {1}-inverses of matrices over PID

被引:5
|
作者
Bu C. [1 ]
机构
[1] Department of Applied Mathematics, School of Science, Harbin Engineering University
关键词
linear preserver; PID(principal ideal domain); {1}-inverse of matrix;
D O I
10.1007/BF02832051
中图分类号
学科分类号
摘要
Let R be a PID,chR = 2,n > 1, M n(R) be then xn full matrix algebra over R.f denotes any invertible linear map preserving {1}-inverses from M n(R) to itself. In this paper, we have proven thatf is an invertible linear map on M n(R) preserving {1}-inverses if and only iff satisfies any one of the following two conditions: (i) there exists a matrixP ε GL n(R) such that f(A) =PAP -1 for allA ε M n(R), (ii) there exists a matrixP ε GL n(R) such thatf(A) =PA t P -1 forA ε M n(R). © 2006 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.
引用
收藏
页码:255 / 265
页数:10
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