A family of geometric means of positive matrices and some new connections - Al Zhour, Zeyad Abdel Al Ziz; Kilicman, Adem (2005)
In this paper, a family of geometric means for positive matrices is studied; provided some counter examples are given. It stills an open problem to find a completely satisfactory definition. We generalize the geometric means of two positive matrices to arrive the definitions of the weighted means of k positive matrices. Some new connections between the Tracy-Singh product and geometric means of positive matrices are established. The results lead to the case of Kronecker product of positive matrices.