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

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 appli...

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Main Authors:	Markiewicz Augustyn, Puntanen Simo
Format:	Article
Language:	English
Published:	De Gruyter 2015-01-01
Series:	Open Mathematics
Subjects:	Best linear unbiased estimator Column space Generalized inverse Linear statistical model Orthocomplement Orthogonal projector
Online Access:	http://www.degruyter.com/view/j/math.2015.13.issue-1/math-2015-0005/math-2015-0005.xml?format=INT

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spelling	doaj-f2a3c1e76eab410e967655c768db589b2020-11-24T20:42:57ZengDe GruyterOpen Mathematics2391-54552015-01-0113110.1515/math-2015-0005math-2015-0005All about the ⊥ with its applications in the linear statistical modelsMarkiewicz Augustyn0Puntanen Simo1Department of Mathematical and Statistical Methods, Pozna´n University of Life Sciences, Wojska Polskiego 28, PL-60637 Poznan, PolandSchool of Information Sciences, FI-33014 University of Tampere, FinlandFor 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 referenceshttp://www.degruyter.com/view/j/math.2015.13.issue-1/math-2015-0005/math-2015-0005.xml?format=INTBest linear unbiased estimatorColumn spaceGeneralized inverseLinear statistical modelOrthocomplementOrthogonal projector
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Markiewicz Augustyn Puntanen Simo
spellingShingle	Markiewicz Augustyn Puntanen Simo All about the ⊥ with its applications in the linear statistical models Open Mathematics Best linear unbiased estimator Column space Generalized inverse Linear statistical model Orthocomplement Orthogonal projector
author_facet	Markiewicz Augustyn Puntanen Simo
author_sort	Markiewicz Augustyn
title	All about the ⊥ with its applications in the linear statistical models
title_short	All about the ⊥ with its applications in the linear statistical models
title_full	All about the ⊥ with its applications in the linear statistical models
title_fullStr	All about the ⊥ with its applications in the linear statistical models
title_full_unstemmed	All about the ⊥ with its applications in the linear statistical models
title_sort	all about the ⊥ with its applications in the linear statistical models
publisher	De Gruyter
series	Open Mathematics
issn	2391-5455
publishDate	2015-01-01
description	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
topic	Best linear unbiased estimator Column space Generalized inverse Linear statistical model Orthocomplement Orthogonal projector
url	http://www.degruyter.com/view/j/math.2015.13.issue-1/math-2015-0005/math-2015-0005.xml?format=INT
work_keys_str_mv	AT markiewiczaugustyn allaboutthewithitsapplicationsinthelinearstatisticalmodels AT puntanensimo allaboutthewithitsapplicationsinthelinearstatisticalmodels
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All about the ⊥ with its applications in the linear statistical models

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