Further results on generalized and hypergeneralized projectors
J. K. Baksalary1 , O. M. Baksalary2 , X. Liu3 , G. Trenkler4
1 Faculty of Mathematics, Informatics and Econometrics, Zielona Góra University, ul. Podgórna 50, PL 65-246 Zielona Góra, Poland
2 Institute of Physics, Adam Mickiewicz University, ul. Umultowska 85, PL 61-614 Poznań, Poland
3 College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, People’s Republic of China
4 Department of Statistics, University of Dortmund, Vogelpothsweg 87, D-44221 Dortmund, Germany
Linear Algebra and its Applications, 429, 1038 (2008)
The notions of generalized and hypergeneralized projectors, introduced by Groß and Trenkler [J. Groß, J. Trenkler, Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997) 463–474], are revisited. On the one hand, the present paper provides several new characterizations of these sets, and, on the other, the properties of generalized and hypergeneralized projectors related to various matrix partial orderings are considered. Moreover, the paper demonstrates the usefulness, in studying the properties of generalized and hypergeneralized projectors, of the representation of complex matrices given in Corollary 6 by Hartwig and Spindelböck [R.E. Hartwig, K. Spindelböck, Matrices for which A* and A† commute, Linear and Multilinear Algebra 14 (1984) 241-256].