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 applic...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2015-01, Vol.13 (1)
Main Authors: Markiewicz, Augustyn, Puntanen, Simo
Format: Article
Language:English
Subjects:
Best linear unbiased estimator
Column space
Generalized inverse
Linear statistical model
Mathematical analysis
Matrices (mathematics)
Orthocomplement
Orthogonal projector
Orthogonality
Statistical models
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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
2391-5455
DOI:10.1515/math-2015-0005