A note on some extensions of the matrix angular central Gaussian distribution

This paper extends the notion of the matrix angular central distribution (MACG) to the complex case. We start by considering the normally distributed random complex matrix ($Z$) and show that is the orientation ($H_Z=Z(Z^{\mathrm{\prime }}Z{)}^{-1}$) has complex MACG (CMACG) distribution. Then we discuss the distribution of the orientation of the linear transformation of the random matrix which orientation part has CMACG distribution. Finally, we discuss the family of distributions which lead to the CMACG distribution.