×

Characterizations of partial isometries and two special kinds of EP elements. (English) Zbl 1524.16066

Summary: We give some sufficient and necessary conditions for an element in a ring to be an EP element, partial isometry, normal EP element and strongly EP element by using solutions of certain equations.

MSC:

16U99 Conditions on elements
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
15A09 Theory of matrix inversion and generalized inverses
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Baksalary, O. M.; Styan, G. P. H.; Trenkler, G., On a matrix decomposition of Hartwig and Spindelböck, Linear Algebra Appl. 430 (2009), 2798-2812 · Zbl 1180.15004 · doi:10.1016/j.laa.2009.01.015
[2] Baksalary, O. M.; Trenkler, G., Characterizations of EP, normal, and Hermitian matrices, Linear Multilinear Algebra 56 (2008), 299-304 · Zbl 1151.15023 · doi:10.1080/03081080600872616
[3] Ben-Israel, A.; Greville, T. N. E., Generalized Inverses: Theory and Applications, CMS Books in Mathematics/Ouvrages de Mathèmatiques de la SMC 15, Springer, New York (2003) · Zbl 1026.15004 · doi:10.1007/b97366
[4] Chen, W., On EP elements, normal elements and partial isometries in rings with involution, Electron. J. Linear Algebra 23 (2012), 553-561 · Zbl 1266.16044 · doi:10.13001/1081-3810.1540
[5] Cheng, S.; Tian, Y., Two sets of new characterizations for normal and EP matrices, Linear Algebra Appl. 375 (2003), 181-195 · Zbl 1054.15022 · doi:10.1016/S0024-3795(03)00650-5
[6] Harte, R.; Mbekhta, M., On generalized inverses in \(C^*\)-algebras, Stud. Math. 103 (1992), 71-77 · Zbl 0810.46062 · doi:10.4064/sm-103-1-71-77
[7] Hartwig, R. E.; Spindelböck, K., Matrices for which \(A^*\) and \(A^{\dagger}\) commute, Linear Multilinear Algebra 14 (1983), 241-256 · Zbl 0525.15006 · doi:10.1080/03081088308817561
[8] Koliha, J. J.; Djordjević, D.; Cvetković, D., Moore-Penrose inverse in rings with involution, Linear Algebra Appl. 426 (2007), 371-381 · Zbl 1130.46032 · doi:10.1016/j.laa.2007.05.012
[9] Mosić, D.; Djordjević, D. S., Moore-Penrose-invertible normal and Hermitian elements in rings, Linear Algebra Appl. 431 (2009), 732-745 · Zbl 1186.16046 · doi:10.1016/j.laa.2009.03.023
[10] Mosić, D.; Djordjević, D. S., Partial isometries and EP elements in rings with involution, Electron. J. Linear Algebra 18 (2009), 761-772 · Zbl 1192.16039 · doi:10.13001/1081-3810.1343
[11] Mosić, D.; Djordjević, D. S., Further results on partial isometries and EP elements in rings with involution, Math. Comput. Modelling 54 (2011), 460-465 · Zbl 1225.15008 · doi:10.1016/j.mcm.2011.02.035
[12] Mosić, D.; Djordjević, D. S., New characterizations of EP, generalized normal and generalized Hermitian elements in rings, Appl. Math. Comput. 218 (2012), 6702-6710 · Zbl 1251.15008 · doi:10.1016/j.amc.2011.12.030
[13] Mosić, D.; Djordjević, D. S.; Koliha, J. J., EP elements in rings, Linear Algebra Appl. 431 (2009), 527-535 · Zbl 1186.16047 · doi:10.1016/j.laa.2009.02.032
[14] Penrose, R., A generalized inverse for matrices, Proc. Camb. Philos. Soc. 51 (1955), 406-413 · Zbl 0065.24603 · doi:10.1017/S0305004100030401
[15] Xu, S.; Chen, J.; Benítez, J., EP elements in rings with involution, Available at https://arxiv.org/abs/1602.08184 (2017), 18 pages
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.