On commutativity of projectors
Radosław Kala
Discussiones Mathematicae Probability and Statistics, Tome 28 (2008), p. 157-165 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:277063 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1098,
     author = {Rados\l aw Kala},
     title = {On commutativity of projectors},
     journal = {Discussiones Mathematicae Probability and Statistics},
     volume = {28},
     year = {2008},
     pages = {157-165},
     zbl = {1158.15012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1098}
}

Radosław Kala. On commutativity of projectors. Discussiones Mathematicae Probability and Statistics, Tome 28 (2008) pp. 157-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1098/

[000] [1] C.R. Rao and M.B. Rao, Matrix Algebra and Its Applications to Statistics and Econometrics, World Scientific, Singapore 2001.

[001] [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.

[002] [3] J.K. Baksalary and R. Kala, Two relations between oblique and Λ-orthogonal projectors, Linear Algebra Appl. 24 (1979), 99-103. | Zbl 0401.15004

[003] [4] C.R. Rao, Projectors, generalized inverses and the BLUE's, J. Roy. Statist. Soc. Ser. B 36 (1974), 442-448. | Zbl 0291.62077

[004] [5] J.K. Baksalary and O.M. Baksalary, Commutativity of projectors, Linear Algebra Appl. 341 (2002), 129-142. | Zbl 0997.15011

[005] [6] J.K. Baksalary, O.M. Baksalary and T. Szulc, A property of ortogonal projectors, Linear Algebra Appl. 354 (2002), 35-39. | Zbl 1025.15039

[006] [7] C.R. Rao and S.K. Mitra, Generalized Inverses of Matrices and Its Applications, Wiley, New York 1971. | Zbl 0236.15004

[007] [8] J. Gross and G. Trenkler, On the product of oblique projectors, Linear Multilinear Algebra 44 (1998), 247-259. | Zbl 0929.15016

[008] [9] Y. Takane and H. Yanai, On oblique projectors, Linear Algebra Appl. 289 (1999), 297-310.