Linear preservers of rank permutability Original Research Article

Let F be an arbitrary field and kgreater-or-equal, slanted2 be an arbitrary fixed integer. A k-tuple of matrices A1,…,Akset membership, variantMn(F) is called rank permutable if rk(A1A2cdots, three dots, centeredAk)=rk(Aσ(1)Aσ(2)cdots, three dots, centeredAσ(k)) for all σset membership, variantSk, where Sk is a symmetric group on k elements. We investigate the set of linear operators on Mn(F) that preserve the set of rank permutable matrix k-tuples.