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An alternative approach to characterize the commutativity of orthogonal projectors

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Baksalary O., Trenkler G.
Discussiones Mathematicae Probability and Statistics
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2008
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tom 28
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nr 1
113-137
EN
In an invited paper, Baksalary [Algebraic characterizations and statistical implications of the commutativity of orthogonal projectors. In: T. Pukkila, S. Puntanen (Eds.), Proceedings of the Second International Tampere Conference in Statistics, University of Tampere, Tampere, Finland, [2], pp. 113-142] presented 45 necessary and sufficient conditions for the commutativity of a pair of orthogonal projectors. Basing on these results, he discussed therein also statistical aspects of the commutativity with reference to problems concerned with canonical correlations and with comparisons between estimators and between sets of linearly sufficient statistics corresponding to different linear models. In the present paper, parts of this analysis are resumed in order to shed some additional light on the problem of commutativity. The approach utilized is different than the one used by Baksalary, and is based on representations of projectors in terms of partitioned matrices. The usefulness of such representations is demonstrated by reinvestigating some of Baksalary's statistical considerations.
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Some comments on the diversity of Vermeer paintings depicted on postage stamps

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Baksalary O., Styan G.
Discussiones Mathematicae Probability and Statistics
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2008
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tom 28
|
nr 1
65-83
EN
We present some comments on the diversity of the paintings by Johannes Vermeer (1632-1675) depicted on postage stamps. We have found 20 of the 36 "recognized" Vermeer paintings depicted on postage stamps issued by 29 "countries"; by country we mean here a stamp-issuing region that issues or has issued its own postage stamps. We apply Fisher's α index of biodiversity [11] to compare the diversity of Vermeer paintings depicted on postage stamps with the diversity of two other data sets [26]. We illustrate our article with images of 7 Vermeer paintings depicted on 10 postage stamps issued by 5 different countries.
3
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Some comments on the life and publications of Jerzy K. Baksalary (1944-2005)

100%
Baksalary O., Styan G.
Discussiones Mathematicae Probability and Statistics
|
2008
|
tom 28
|
nr 1
5-64
EN
Following some biographical information on Jerzy K. Baksalary (1944-2005) and some comments by Tadeusz Caliński, Oskar Maria Baksalary, and Image Editors-in-Chief: Bryan L. Shader and Hans Joachim Werner, this article continues with personal remarks on the life and publications of Jerzy K. Baksalary by Anita Dobek, R. William Farebrother, Jürgen Groß, Jan Hauke, Radosław Kala, Erkki Liski, Xiaoji Liu, Augustyn Markiewicz, Thomas Mathew, Wiesław Migdałek, Friedrich Pukelsheim, Tarmo Pukkila, Simo Puntanen, C. Radhakrishna Rao, Dietrich von Rosen, George P.H. Styan, Tomasz Szulc, Yongge Tian, Götz Trenkler, Frank Uhlig, Júlia Volaufová, Haruo Yanai, and Fuzhen Zhang. These remarks are followed by a detailed list of Jerzy Baksalary's publications prepared by the editors of this article.
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