Multi-Input Multi-Output (MIMO) transmission has been a topic of great interest for a few years due to the huge spectral efficiency gain it can provide over rich scattering transmission channels, such as indoor (e.g. wireless local area networks) or urban outdoor (e.g. mobile wireless communications). MIMO transmission channels are usually modelled by random matrices. In this paper, we use results from random matrices theory to derive the statistics of the smallest singular value of a MIMO channel. Indeed, the smallest singular value is of crucial importance for the performances of the transmission system because it determines the minimum distance between the received vectors.