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On formulae for the Moore–Penrose inverse of a columnwise partitioned matrix

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  • Baksalary, Oskar Maria
  • Trenkler, Götz

Abstract

The paper revisits the considerations carried out in [J.K. Baksalary, O.M. Baksalary, Linear Algebra Appl. 421 (2007) 16–23], where particular formulae for the Moore–Penrose inverse of a columnwise partitioned matrix were derived. An impuls to reconsider these investigations originated from a number of recently published articles in which the results established by Baksalary and Baksalary were utilized in different research areas of applicable background. In the present paper several not exposed so far consequences of the results derived in the recalled paper are unveiled, with an emphasis placed on revealing their underlying applicability capabilities. A special attention is paid to the computational aspects of the Moore–Penrose inverse determination.

Suggested Citation

  • Baksalary, Oskar Maria & Trenkler, Götz, 2021. "On formulae for the Moore–Penrose inverse of a columnwise partitioned matrix," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    • Handle: RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300320308663
    DOI: 10.1016/j.amc.2020.125913
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    References listed on IDEAS

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    1. Magnus, J.R., 1990. "On the fundamental bordered matrix of linear estimation," Other publications TiSEM b4e18af6-b9d7-49ca-8e07-5, Tilburg University, School of Economics and Management.
    2. Oskar Baksalary & Götz Trenkler, 2009. "A projector oriented approach to the best linear unbiased estimator," Statistical Papers, Springer, vol. 50(4), pages 721-733, August.
    3. Herrero, A. & Thome, N., 2020. "Sharp partial order and linear autonomous systems," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    4. van Der Ploeg, Frederick (ed.), 1990. "Advanced Lectures in Quantitative Economics," Elsevier Monographs, Elsevier, edition 1, number 9780127117034.
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    1. Oskar Maria Baksalary & Götz Trenkler, 2022. "An alternative look at the linear regression model," Statistical Papers, Springer, vol. 63(5), pages 1499-1509, October.

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