A Note on Some Extensions of the Matrix Angular Central Gaussian Distribution
DOI:
https://doi.org/10.24425/cejeme.2025.156674Keywords:
complex Stiefel manifold, matrix angular central Gaussian distributionAbstract
In this paper, we extend the concept of a matrix angular central Gaussian (MACG) distribution to the complex domain. First, we consider a normally distributed random complex matrix (Z) and demonstrate that its orientation (HZ = Z(Z¯0Z)−1/2) exhibits a complex MACG (CMACG) distribution. We then discuss the distribution of the orientation of the linear transformation of the random matrix, the orientation of which has a CMACG distribution. Finally, we examine the family of distributions that leads to the CMACG distribution.
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