保持半环上矩阵{1,2}-逆的可逆线性算子

The Invertible Linear Operator Preserving {1,2}-Inverses of Matrices over Semirings

摘要: 线性保持问题一直是矩阵论研究中一个较为活跃的课题。本文主要研究了保持半环上矩阵{1,2}-逆的可逆线性算子。完全的刻画了保持链半环、非负整数环和非负实数环上的矩阵{1,2}-逆的可逆算子。

Abstract: Linear preserve problem has been a relatively active topic in the matrix theory research. In the paper, we mainly study invertible linear operators that preserve {1,2}-inverses of matrices over semirings. It is completely characterized that invertible linear operators which preserve {1,2}- inverse of matrices over chain semiring, the nonnegative integers, and the nonnegative reals.