Hua’s fundamental theorems of the geometry of matrices and related results

AbstractWe briefly survey some recent improvements of Hua’s fundamental theorem of the geometry of rectangular matrices. Then we discuss possible further generalizations as well as some related open problems in the theory of preservers. We solve one such open problem using Ovchinnikov’s characterization of automorphisms of the poset of idempotent matrices. Using Ovchinnikov’s result we obtain a short proof of the fundamental theorem of the geometry of square matrices