Congruential automorphism groups of general matrices

Abstract

For A∈M n( C) , Aut( A), the congruential automorphism group of A, is the set of all non-singular C∈M n( C) such that C ∗AC=A. Here, the A for which Aut( A) is bounded are described, and this allows the characterization of pairs A, B for which the set of matrices carrying the congruence of A to B is compact. This characterization is in terms of non-singular unitoid matrices in which certain configurations of canonical angles are forbidden.