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The complex Empirical Orthogonal Function (CEOF) analysis has been extensively used in the meteorological and oceanic fields, and the key part of this method is to extract eigenvalues, eigenvectors, and complex principal components from a Hermite matrix. In previous studies, however, no one explores statistical and physical significances of the resolution of a Hermite Matrix. It is demonstrated that the eigenvalues of a complex Hermite Matrix represent variance contribution or anomalous energy, and eigenvectors have clear statistical significances and no apparent physical significances. In contrast, a complex principal component has a clear physical significance, and their real and imaginary parts are related to each other. Thus, the dimensional linear regression method can be used to extract predominant modes of vector variability.