Abstract

GUPTA, Arjun K.; NAGAR, Daya K.  and  VELEZ-CARVAJAL, Astrid M.. Unitary invariant and residual independent matrix distributions. Comput. Appl. Math. [online]. 2009, vol.28, n.1, pp. 63-86. ISSN 1807-0302.  http://dx.doi.org/10.1590/S0101-82052009000100004.

Define Z₁₃ = A^1/2Y(A^1/2)^H (A and Y are independent) and Z₁₅ = B^1/2Y(B^1/2)^H (B and Y are independent), where Y, A and B follow inverted complex Wishart, complex beta type I and complex beta type II distributions, respectively. In this article several properties including expected values of scalar and matrix valued functions of Z₁₃ and Z₁₅ are derived.

Keywords : beta distribution; inverted complex Wishart; complex random matrix; Gauss hypergeometric function; residual independent; unitary invariant; zonal polynomial.