Abstract
The notions of generalized and hypergeneralized projectors, introduced by Groβ and Trenkler [Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997) 463–474], attracted recently considerable attention. The list of publications devoted to them comprises now over ten positions, and the present paper briefly discusses some of the results available in the literature. Furthermore, several new characteristics of generalized and hypergeneralized projectors are established with the use of Corollary 6 in Hartwig and Spindelböck [Matrices for which A* and A† commute. Linear Multilinear Algebra 14 (1984) 241–256].
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References
Baksalary, J.K., Baksalary, O.M.: On linear combinations of generalized projectors. Linear Algebra Appl. 388, 17–24 (2004)
Baksalary, J.K., Baksalary, O.M., Groβ, J.: On some linear combinations of hypergeneralized projectors. Linear Algebra Appl. 413, 264–273 (2006)
Baksalary, J.K., Baksalary, O.M., Liu, X.: Further properties of generalized and hypergeneralized projectors. Linear Algebra Appl. 389, 295–303 (2004)
Baksalary, J.K., Baksalary, O.M., Liu, X., Trenkler, G.: Further results on generalized and hypergeneralized projectors. Linear Algebra Appl. 429, 1038– 1050 (2008)
Baksalary, J.K., Liu, X.: An alternative characterization of generalized projectors. Linear Algebra Appl. 388, 61–65 (2004)
Baksalary, O.M., Benítez, J.: On linear combinations of two commuting hy-pergeneralized projectors. Computers & Mathematics with Applications 56, 2481–2489 (2008) (Dedicated to Professor Götz Trenkler on the occasion of his 65th birthday.)
Baksalary, O.M., Trenkler, G.: Characterizations of EP, normal, and Hermitian matrices. Linear Multilinear Algebra 56, 299–304 (2008)
Baksalary, O.M., Trenkler, G.: Problem 37-2 “Rank of a generalized projector”. IMAGE 37, 32 (2006)
Baksalary, O.M., Trenkler, G.: Problem “A Property of the Range of Generalized and Hypergeneralized Projectors”. IMAGE. Submitted.
Benítez, J., Thome, N.: Characterizations and linear combinations of k-generalized projectors. Linear Algebra Appl. 410, 150–159 (2005)
Du, H.-K., Li, Y.: The spectral characterization of generalized projections. Linear Algebra Appl. 400, 313–318 (2005)
Du, H.-K., Wang, W.-F., Duan, Y.-T.: Path connectivity of k-generalized projectors. Linear Algebra Appl. 422, 712–720 (2007)
Groβ, J., Trenkler, G.: Generalized and hypergeneralized projectors. Linear Algebra Appl. 264, 463–474 (1997)
Hartwig, R.E., Spindelböck, K.: Matrices for which A* and A† commute. Linear Multilinear Algebra 14, 241–256 (1984)
Lebtahi, L., Thome, N.: A note on k-generalized projectors, Linear Algebra Appl. 420, 572–575 (2007)
Meyer, C.D.: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia (2000)
Stewart, G.W.: A note on generalized and hypergeneralized projectors. Linear Algebra Appl. 412, 408–411 (2006)
Trenkler, G.: On oblique and orthogonal projectors. In: Brown, P., Liu, S., Sharma, D. (eds.) Contributions to Probability and Statistics: Applications and Challenges, Proceedings of the International Statistics Workshop, pp. 178– 191. World Scientific, Singapore (2006)
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Baksalary, O.M. (2009). Revisitation of Generalized and Hypergeneralized Projectors. In: Schipp, B., Kräer, W. (eds) Statistical Inference, Econometric Analysis and Matrix Algebra. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2121-5_21
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DOI: https://doi.org/10.1007/978-3-7908-2121-5_21
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