Γ-Commuting triples of positive definite matrices and midpoint equations on unitary matrices Original Research Article

Triples of positive definite matrices that can be transformed to a commuting triple by a congruence transformation are called Γ-commuting. In this paper we give various descriptions and characterizations of Γ-commuting triples and particularly focus on those involving the geometric mean and midpoint equations on a generating set of the special unitary group.