2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185732We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^\dagger A$, for any finite number of rows and columns of $A$, 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 of reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.11 pages; v2: references updated + some clarifications added; v3: version to appear in J. Phys. A, Special Issue on Random Matrix TheoryMathematical PhysicsCondensed MatterHigh Energy Physics - TheoryChaotic Dynamicstext