# What is the relation between singular correlation matrix and PCA?

Can anyone kindly give me some information about the statement (last sentence) at the end of below definition. What does it mean by "It can be used when a correlation matrix is singular"? This quote is from SPSS help menu on factor analysis.

Principal Components Analysis. A factor extraction method used to form uncorrelated linear combinations of the observed variables. The first component has maximum variance. Successive components explain progressively smaller portions of the variance and are all uncorrelated with each other. Principal components analysis is used to obtain the initial factor solution. It can be used when a correlation matrix is singular.

I already know that different from other factor extraction methods, PCA uses total variance in data while extracting factors. Is it somehow related to this?

• +1. But can't "principal factor" extraction method (iterating updates of uniquenesses $\Psi$ and updates of loadings via PCA of reduced covariance matrix $C-\Psi$) be applied to low-rank covariance matrices as well? I don't see anything in this simple iterative procedure that would fail when $C$ is low rank. – amoeba says Reinstate Monica Mar 23 '15 at 14:54