Automorphisms of Mn, partially ordered by rank subtractivity ordering Original Research Article

Let Mn be the space of all n×n matrices with coefficients in image or image, where ngreater-or-equal, slanted3. The rank subtractivity or minus partial order on Mn is defined by Aless-than-or-equals, slantrsB iff rank B=rank A+rank(B−A). We characterize bijective mappings Φ on Mn such that Aless-than-or-equals, slantrsB iff Φ(A)less-than-or-equals, slantrsΦ(B) (A,Bset membership, variantMn).