Abstract
We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices 
†, for any finite number of rows and columns of , without any large N approximations. In particular, we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure for reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.