Random Correlation Matrices and One Decomposition of the Wishart Distribution

In the proposed article, random matrices whose distribution coincides with the Wishart distribution are considered.Their elements, which are dependent, are represented as algebraic functions of independent random variables.The densities of the independent random variables are also indicated.A Wishart matrix construction is thus obtained.The present paper shows the relationship between the proposed Wishart matrix construction and correlations and partial correlations.The considered construction was also used to obtain a factorization of the determinant of a correlation matrix.