# On commutativity of projectors

Discussiones Mathematicae Probability and Statistics (2008)

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

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topRadosław 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] C.R. Rao and M.B. Rao, Matrix Algebra and Its Applications to Statistics and Econometrics, World Scientific, Singapore 2001.
- [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] J.K. Baksalary and R. Kala, Two relations between oblique and Λ-orthogonal projectors, Linear Algebra Appl. 24 (1979), 99-103. Zbl0401.15004
- [4] C.R. Rao, Projectors, generalized inverses and the BLUE's, J. Roy. Statist. Soc. Ser. B 36 (1974), 442-448. Zbl0291.62077
- [5] J.K. Baksalary and O.M. Baksalary, Commutativity of projectors, Linear Algebra Appl. 341 (2002), 129-142. Zbl0997.15011
- [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] C.R. Rao and S.K. Mitra, Generalized Inverses of Matrices and Its Applications, Wiley, New York 1971. Zbl0236.15004
- [8] J. Gross and G. Trenkler, On the product of oblique projectors, Linear Multilinear Algebra 44 (1998), 247-259. Zbl0929.15016
- [9] Y. Takane and H. Yanai, On oblique projectors, Linear Algebra Appl. 289 (1999), 297-310.

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