A reflexive generalized inverse and the Moore-Penrose inverse are often confused in statistical literature but in fact they have completely different behaviour in case the population covariance matrix is not a multiple of identity. In this paper, we study the spectral properties of a reflexive generalized inverse and of the Moore-Penrose inverse of the sample covariance matrix. The obtained results are used to assess the difference in the asymptotic behaviour of their eigenvalues.
CITATION STYLE
Bodnar, T., & Parolya, N. (2020). Spectral analysis of large reflexive generalized inverse and Moore-Penrose inverse matrices. In Recent Developments in Multivariate and Random Matrix Analysis: Festschrift in Honour of Dietrich von Rosen (pp. 1–16). Springer International Publishing. https://doi.org/10.1007/978-3-030-56773-6_1
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