Spectral Analysis of Large Reflexive Generalized Inverse and Moore-Penrose Inverse Matrices

Taras Bodnar; N. Parolya

doi:10.1007/978-3-030-56773-6_1

Spectral Analysis of Large Reflexive Generalized Inverse and Moore-Penrose Inverse Matrices

Taras Bodnar^*
, N. Parolya

^*Corresponding author for this work

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Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

3 Citations (Scopus)

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Abstract

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.

Original language	English
Title of host publication	Recent Developments in Multivariate and Random Matrix Analysis
Subtitle of host publication	Festschrift in Honour of Dietrich von Rosen
Editors	Thomas Holgersson, Martin Singull
Place of Publication	Cham
Publisher	Springer
Pages	1-16
Number of pages	16
ISBN (Electronic)	978-3-030-56773-6
ISBN (Print)	978-3-030-56772-9
DOIs	https://doi.org/10.1007/978-3-030-56773-6_1
Publication status	Published - 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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Spectral Analysis of Large Reflexive Generalized Inverse and Moore-Penrose Inverse Matrices. / Bodnar, Taras; Parolya, N.
Recent Developments in Multivariate and Random Matrix Analysis: Festschrift in Honour of Dietrich von Rosen. ed. / Thomas Holgersson; Martin Singull. Cham: Springer, 2020. p. 1-16.

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

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Spectral Analysis of Large Reflexive Generalized Inverse and Moore-Penrose Inverse Matrices

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