We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant operator. Specifically, we derive compact expressions for the joint probability distribution function of the eigenvalues and the expectation of functions of the eigenvalues, including joint moments, for the case of both ordered and unordered eigenvalues.

中文翻译：

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关于某些有限维随机矩阵的特征值的任意子集的分布

我们使用张量伪行列式算子对有限维复数 Wishart、双 Wishart 和高斯厄米特随机矩阵的有序特征值的任意子集的联合分布提出了一些新结果。具体来说，对于有序和无序特征值的情况，我们推导出特征值的联合概率分布函数和特征值函数的期望（包括联合矩）的紧凑表达式。