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? 
 A: The citation and its last sentence says of the following.
Singular matrix is a one where rows or columns are linearly interdependent. Most of factor analysis extraction methods require that the analyzed correlation or covariance matrix be nonsingular. It must be strictly positive definite. The reasons for it is that at various stages of the analysis (preliminary, extraction, scores) factor analysis algorithm addresses true inverse of the matrix or needs its determinant. Minimal residuals (minres) method can work with singular matrix at extraction, but it is absent in SPSS.
PCA is not iterative and is not true factor analysis. Its extraction phase is single eigen-decomposition of the intact correlation matrix, which doesn't require the matrix to be full rank. Whenever it is not, one or several last eigenvalues turn out to be exactly zero rather than being small positive. Zero eigenvalue means that the corresponding dimension (component) has variance 0 and therefore does not exist. That's all; it doesn't hamper the extraction, nor it precludes computing component scores. So, you can do PCA with singular, multicollinear data. Sometimes PCA is used specifically for the purpose to get rid of the multicollinearity.
A: It's related to the mathematical property of the correlation matrix. 
In simple words, PCA is essentially an orthogonal transformation of the given correlation matrix, which can be either invertible or singular (I.e. doesn't have an inverse matrix).
