Preservers of matrix pairs with bounded distance Original Research Article

Let m, n and k be positive integers such that 2 less-than-or-equals, slant k < n less-than-or-equals, slant m. Let V denote either the vector space of all m × n matrices over a field with at least three elements or the vector space of all n × n Hermitian matrices over a field F of characteristic ≠ 2 associated with an involution. We characterize surjective mappings T from V onto itself such that for every pair A, B set membership, variant V, rank(A − B) less-than-or-equals, slant k if and only if rank(T(A) − T(B)) less-than-or-equals, slantk.