Geometric mean decomposition (GMD) has been proposed as an elegant tool for MIMO transceiver architecture design. Under the ideal assumptions, MIMO-GMD schemes can realize multiple spatial sub-channels with identical gains. The main goal of this paper is to provide analytical distribution functions for sub-channels gains and capacities of MIMO-GMD schemes. In particular, we have derived closed-form results for MIMO-GMD transceivers with two spatial streams. Furthermore, we show that the sub-channel gains for cases with arbitrary number of spatial streams can be approximated by Gamma random variables with excellent accuracy. Additionally, some practical applications of these results are also presented in this paper.