Preserving Rank Export Matrix Space Mapping

The matrix algebra as an important research area of algebra has wide appli-cations in many areas. Linear preserver problems(LPPs for short) has been a veryactive area of matrix algebra during the last several years. Many excellent resultshave appeared .Let (?) be maps from F to itself.(?)At present, produced map of preserving rank(preserving rank-1) in quadratematrices space!upper triangular matrices space and symmetric matrices space havegained clear results.Inspired by them,this article studied produced map of preservingrank-2 in alternate matrices space, and the main result of the article is that if f isthe map produced by fij(i,j = 1, 2,...,n) in Kn(F)(n≥4) with f(0) = 0, then thenecessary and su?cient condition of f preserving rank 2 is that exist nonsingularand diagonal matrix (?) such that(?)where ? is a single domain from the same state.In graduation thesis, Sunshulan described the produced map of Sn(F) withn > 2 in 2007.Making up for its lack,the article gives the form of produced map ofpreserving rank-1 in S2(C) at the end.