Linear maps preserving M–P inverses of matrices between matrix spaces over fields

Abstract

Suppose F is a field of characteristic not 2. Let n and m be two arbitrary positive integers with n≥2. We denote by Mn(F) and Sn(F) the space of n×n full matrices and the space of n×n symmetric matrices over F, respectively. All linear maps from Sn(F) to Mm(F) preserving M–P inverses of matrices are characterized first, and thereby all linear maps from Sn(F) (Mn(F)) to Sm(F) (Mm(F)) preserving M–P inverses of matrices are characterized, respectively.