Numerical Analysis of a Correlation Matrix
Thierry Foucart · Statistics · 1997
In this paper we present some new results on a definite positive symmetric matrix: We prove that each term of such a matrix belongs to an interval which depends on the other ones and we give a relation between entries, the interval in which each entry belongs to, and the corresponding entry of the inverse matrix. So these properties give a new interpretation in the case of correlation matrices: correlation coefficients are bounded given the other ones, and partial correlation coefficients are defined from the intervals. We finally give numerical examples computed by programs available from the author.