Goodman derived the complex Hishart distribution with the aid of characteristic functions and Fourier transforms. From this the distribution of the complex rectangular co-ordinates were derived as an application of the complex Hishart distribution. In the present paper we give a direct and simplified method of deriving the distribution of the complex rectangular co-ordinates. From this distribution the complex Hishart distribution will be derived as an application. Some properties of the distribution of the complex rectangular coordinates will be given. In addition some applications and in particular the application of the distribution in the derivation of the distribution of the "complex" generalized variance will also be given.

This thesis attempts to isolate the major markets for investment outside South Africa, and to determine what proportion of a South African investor's capital, if any, should be held in foreign securities under different possible restrictions laid down by the South African Reserve Bank. The main argument advanced in favour of foreign investment is risk reduction through diversification.

Bibliography: pages 311-318. / In this study the distributional properties of certain multivariate complex quadratic forms and their characteristic roots are investigated. Multivariate complex distribution theory was originally introduced by Wooding (1956), Turin (1960) and Goodman (1963a) when they derived and studied the multivariate complex normal distribution. The multivariate complex normal distribution is the basis of complex distribution theory and plays an important role in various areas. In the area of multiple time-series the complex distribution theory is found very useful.