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A reflexive generalized inverse and the Moore-Penrose inverse are oftenconfused in statistical literature but in fact they have completely differentbehaviour in case the population covariance matrix is not a multiple ofidentity. In this paper, we study the spectral properties of a reflexivegeneralized inverse and of the Moore-Penrose inverse of the sample covariancematrix. The obtained results are used to assess the difference in theasymptotic behaviour of their eigenvalues.

Spectral analysis of large reflexive generalized inverse and Moore-Penrose inverse matrices