Wishart and Anti-Wishart random matrices

Details Wishart and Anti-Wishart random matrices Wishart and Anti-Wishart random matrices

2001-12-10

arxiv.org/abs/math-ph/0112017v3

J.Phys.A36:3629-3638,2003

Physics

Mathematical Physics

11 pages; v2: references updated + some clarifications added; v3: version to appear in J. Phys. A, Special Issue on Random Mat

Scientific paper

10.1088/0305-4470/36/12/343

We 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.

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