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.
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Acknowledgements
The authors are very grateful to two anonymous referees whose remarks improved the presentation of the paper.
The final version of this paper was prepared while the first author was visiting the Faculty of Statistics at the Dortmund University of Technology. The financial supports from the Alexander von Humboldt Foundation as well as from the project POKL run at the Faculty of Physics of the Adam Mickiewicz University are gratefully acknowledged. The author is also very thankful to the Faculty of Statistics for provision of excellent facilities during the stay.
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Baksalary, O.M., Trenkler, G. (2013). On the Entries of Orthogonal Projection Matrices. In: Bapat, R., Kirkland, S., Prasad, K., Puntanen, S. (eds) Combinatorial Matrix Theory and Generalized Inverses of Matrices. Springer, India. https://doi.org/10.1007/978-81-322-1053-5_9
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DOI: https://doi.org/10.1007/978-81-322-1053-5_9
Publisher Name: Springer, India
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