Positive semidefinite Bounds regarding Correlation Matrices

The note provides an analysis and implementation of selected aspects regarding positive semidefinite bounds with respect to correlation matrices. More specifically a single correlation value between two random variables will be varied, while maintaining all other correlations (denoted as “defaults”) constant. In addition all correlations, except for one single correlation value will be subject to variation. For sake of consistency and comparability all default correlations are designed to share the same value. Furthermore the analysis will be conducted for a wide range of correlation matrix dimensions.
After the review of some general properties concerning correlation matrices, the results of the analysis will be addressed. Finally the generated R code - for the purpose of this investigation - will be presented.