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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 13, Issue 1

Issues

Volume 13 (2015)

All about the ⊥ with its applications in the linear statistical models

Augustyn Markiewicz
  • Department of Mathematical and Statistical Methods, Pozna´n University of Life Sciences, Wojska Polskiego 28, PL-60637 Poznan, Poland
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/ Simo Puntanen
Published Online: 2014-10-09 | DOI: https://doi.org/10.1515/math-2015-0005

Abstract

For an n x m real matrix A the matrix A is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

Keywords : Best linear unbiased estimator; Column space; Generalized inverse; Linear statistical model; Orthocomplement; Orthogonal projector

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About the article

Received: 2013-12-13

Accepted: 2014-04-14

Published Online: 2014-10-09

Published in Print: 2015-01-01


Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0005.

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© 2015 Augustyn Markiewicz, Simo Puntanen. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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