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We give a generalization of random matrix ensembles, which includes all classical ensembles. We derive the joint-density function of the generalized ensemble by one simple formula, giving a direct and unified way to compute the density functions for all classical ensembles and various kinds of new ensembles. An integration formula associated with the generalized ensembles is given. We propose a taxonomy of generalized ensembles encompassing all classical ensembles and some new ones not considered before.

A generalization of random matrix ensemble, I: General theory