Correlation Coefficients for Complex Random Vectors

We consider the assessment of multivariate association between two complex random vectors. For complex data, there are three types of correlation coefficients, which account for rotational, reflectional, and total (i.e., rotational and reflectional) dependencies. We define and analyze these three types for different correlation coefficients, based on two popular correlation analysis techniques: canonical correlation analysis and multivariate linear regression (also known as half-canonical correlation analysis).