On commutativity of projectors

• Autorzy: Radosław Kala
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

oblique projector; orthogonal projector; commutativity

Kategorie tematyczne

• 15A27: Commutativity
• 15A03: Vector spaces, linear dependence, rank

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 157-165

Daty

wydano

2008

otrzymano

2007-12-14

Twórcy

autor

Radosław Kala

• Department of Mathematical and Statistical Methods, Agricultural University of Poznań, Wojska Polskiego 28, PL 60-637 Poznań, Poland

Bibliografia

• [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.
• [4] C.R. Rao, Projectors, generalized inverses and the BLUE's, J. Roy. Statist. Soc. Ser. B 36 (1974), 442-448.
• [5] J.K. Baksalary and O.M. Baksalary, Commutativity of projectors, Linear Algebra Appl. 341 (2002), 129-142.
• [6] J.K. Baksalary, O.M. Baksalary and T. Szulc, A property of ortogonal projectors, Linear Algebra Appl. 354 (2002), 35-39.
• [7] C.R. Rao and S.K. Mitra, Generalized Inverses of Matrices and Its Applications, Wiley, New York 1971.
• [8] J. Gross and G. Trenkler, On the product of oblique projectors, Linear Multilinear Algebra 44 (1998), 247-259.
• [9] Y. Takane and H. Yanai, On oblique projectors, Linear Algebra Appl. 289 (1999), 297-310.

Identyfikatory

DOI

10.7151/dmps.1098