Eigenvalues and Eigenvectors of Correlation Matrices with Special Structures: Applications to Factor Analysis of Common Stock Rates of Return

摘要

The authors derive the general forms for the eigenvalues and eigenvectors of certain correlation matrices with special structures. Our inquiry was motivated by an analysis of the rates of return on common stocks. Stocks within certain groups (for example, stocks within the same industry) may be equally correlated and the correlations between stocks in different groups, although equal, may be smaller in magnitude than the within group correlations.