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

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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Bibliographic Details
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
Description
Summary: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
ISSN:2391-5455

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