On the Entries of Orthogonal Projection Matrices

Oskar Maria Baksalary () and Götz Trenkler ()
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Oskar Maria Baksalary: Adam Mickiewicz University, Faculty of Physics
Götz Trenkler: Dortmund University of Technology, Department of Statistics

A chapter in Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013, pp 101-118 from Springer

Abstract: Abstract The present paper is concerned with characterizing entries of orthogonal projectors (i.e., a Hermitian idempotent matrices). On the one hand, several bounds for the values of the entries are identified. On the other hand, particular attention is paid to the question of how an orthogonal projector changes when its entries are modified. The modifications considered are those of a single entry and of an entire row or column. Some applications of the results in the linear regression model are pointed out as well.

Keywords: Orthogonal projector; Idempotent matrices; Oblique projector; Moore–Penrose inverse; Linear model; 15A09; 62J12 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1053-5_9

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DOI: 10.1007/978-81-322-1053-5_9

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