This paper presents an asymptotic analysis of the eigen value decomposition (EVD) of the sample covariance matrix associated with independent identically distributed (IID) non necessarily circular and Gaussian data that extends the well known analysis presented in the literature for circular and Gaussian data. Closed-form expressions of the asymptotic bias and variance of the sample eigenvalues and eigenvectors are given. As an application of these extended expressions, the statistical performance analysis of the minimum description length (MDL) criterion applied to the detection of the number of noncircular or/and nonGaussian components is considered