A Note on Matrix Ill-Conditioning and the Modified Correlation Matrix

The Introductory Overview discusses the issue of matrix ill-conditioning. If during the factoring process you receive the message that the correlation matrix could not be inverted, then, when subsequently calling the Review Descriptive Statistics dialog box, the correlation matrix will have been modified (to allow inversion). Specifically, a small constant was added to the diagonal of the correlation matrix until the determinant of that matrix was greater than 1.e-50. The modified (slightly lowered) correlations will be reported here if matrix ill conditioning was detected and the modification performed.

Additionally, all subsequent computations will be performed based on the modified (slightly lowered) correlations.