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

摘要

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