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abstract: 'We give a generalization of the random matrix ensembles, including all classical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give 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 ensemble is also given. We also give a classification scheme of the generalized ensembles, which will include all classical ensembles and some new ensembles which were not considered before.'
address:
- 'School of mathematical science, Peking University, Beijing, 100871, P. R. China'
- 'School of mathematical science, Peking University, Beijing, 100871, P. R. China '
- 'School of mathematics and physics, Zhejiang Normal University, Zhejiang Jinhua, 321004, P. R. China '
author:
- Jinpeng An
- Zhengdong Wang
- Kuihua Yan
title: 'A Generalization of random matrix ensemble I: general theory$^1$'
---

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Introduction
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0.5cm One of the most fundamental problems in the theory of random matrices is to derive the joint density functions for the eigenvalues (or equivalently, the measures associated with the eigenvalue distributions) of various types of matrix ensembles. In his monograph [@Me], Mehta summarized the classical 