Additive Preservers Of Moore-Penrose Inverses Of Matrices Over Division Rings

Linear preserver problem(LPP) is an important research ?eld in matrix theoryand its applications. It has been widely used in the di?erential equations, systemcontrol and other ?elds. In the recent decades LPP has achieved fruitful results. Thegeneralized inverses of matrices is an important tool for solving linear equations and theresearch on the subject has not been interrupted in the past decades. This article willdescribe the additive maps which preserve the Moore-Penrose inverse from symmetricmatrix space to whole matrix spaces over division rings of characteristic not 2. Themain results obtained are as follows :1: First, we introduce the origin of generalized inverse problems and introduce thedevelopment of Moore-Penrose inverse preservers in detail.2: Next, We present some basic lemmas and propositions, for them some conclu-sions have certain applications to some related ?elds.3: Final, We describe the additive maps which preserve the Moore-Penrose inversefrom symmetric matrix space to whole matrix spaces over division rings of characteristicnot 2 on which an involusion with a trace of nature is equipped.