On commutativity of projectors

Radosław Kala

Discussiones Mathematicae Probability and Statistics (2008)

  • Volume: 28, Issue: 1, page 157-165
  • ISSN: 1509-9423

Abstract

top
It is shown that commutativity of two oblique projectors is equivalent with their product idempotency if both projectors are not necessarily Hermitian but orthogonal with respect to the same inner product.

How to cite

top

Radosław Kala. "On commutativity of projectors." Discussiones Mathematicae Probability and Statistics 28.1 (2008): 157-165. <http://eudml.org/doc/277063>.

@article{RadosławKala2008,
abstract = {It is shown that commutativity of two oblique projectors is equivalent with their product idempotency if both projectors are not necessarily Hermitian but orthogonal with respect to the same inner product.},
author = {Radosław Kala},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {oblique projector; orthogonal projector; commutativity; inner product},
language = {eng},
number = {1},
pages = {157-165},
title = {On commutativity of projectors},
url = {http://eudml.org/doc/277063},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Radosław Kala
TI - On commutativity of projectors
JO - Discussiones Mathematicae Probability and Statistics
PY - 2008
VL - 28
IS - 1
SP - 157
EP - 165
AB - It is shown that commutativity of two oblique projectors is equivalent with their product idempotency if both projectors are not necessarily Hermitian but orthogonal with respect to the same inner product.
LA - eng
KW - oblique projector; orthogonal projector; commutativity; inner product
UR - http://eudml.org/doc/277063
ER -

References

top
  1. [1] C.R. Rao and M.B. Rao, Matrix Algebra and Its Applications to Statistics and Econometrics, World Scientific, Singapore 2001. 
  2. [2] J.K. Baksalary, Algebraic characterizations and statistical implications of the commutativity of orthogonal projectors, pp. 113-142 in: Proceedings of the Second International Tampere Conference in statistics, T. Pukkila, S. Puntanen (Eds.), University of Tampere, Tampere, Finland 1987. 
  3. [3] J.K. Baksalary and R. Kala, Two relations between oblique and Λ-orthogonal projectors, Linear Algebra Appl. 24 (1979), 99-103. Zbl0401.15004
  4. [4] C.R. Rao, Projectors, generalized inverses and the BLUE's, J. Roy. Statist. Soc. Ser. B 36 (1974), 442-448. Zbl0291.62077
  5. [5] J.K. Baksalary and O.M. Baksalary, Commutativity of projectors, Linear Algebra Appl. 341 (2002), 129-142. Zbl0997.15011
  6. [6] J.K. Baksalary, O.M. Baksalary and T. Szulc, A property of ortogonal projectors, Linear Algebra Appl. 354 (2002), 35-39. Zbl1025.15039
  7. [7] C.R. Rao and S.K. Mitra, Generalized Inverses of Matrices and Its Applications, Wiley, New York 1971. Zbl0236.15004
  8. [8] J. Gross and G. Trenkler, On the product of oblique projectors, Linear Multilinear Algebra 44 (1998), 247-259. Zbl0929.15016
  9. [9] Y. Takane and H. Yanai, On oblique projectors, Linear Algebra Appl. 289 (1999), 297-310. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.