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Keywords:
EP element; partial isometry; normal EP element; strongly EP element; solutions of equation
EP element; partial isometry; normal EP element; strongly EP element; solutions of equation
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.
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. DOI 10.1016/j.laa.2009.01.015 | MR 2509859 | Zbl 1180.15004
[2] Baksalary, O. M., Trenkler, G.: Characterizations of EP, normal, and Hermitian matrices. Linear Multilinear Algebra 56 (2008), 299-304. DOI 10.1080/03081080600872616 | MR 2384656 | Zbl 1151.15023
[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). DOI 10.1007/b97366 | MR 1987382 | Zbl 1026.15004
[4] Chen, W.: On EP elements, normal elements and partial isometries in rings with involution. Electron. J. Linear Algebra 23 (2012), 553-561. DOI 10.13001/1081-3810.1540 | MR 2946809 | Zbl 1266.16044
[5] Cheng, S., Tian, Y.: Two sets of new characterizations for normal and EP matrices. Linear Algebra Appl. 375 (2003), 181-195. DOI 10.1016/S0024-3795(03)00650-5 | MR 2013464 | Zbl 1054.15022
[6] Harte, R., Mbekhta, M.: On generalized inverses in $C^{*}$-algebras. Stud. Math. 103 (1992), 71-77. DOI 10.4064/sm-103-1-71-77 | MR 1184103 | Zbl 0810.46062
[7] Hartwig, R. E., Spindelböck, K.: Matrices for which $A^{*}$ and $A^{\dagger}$ commute. Linear Multilinear Algebra 14 (1983), 241-256. DOI 10.1080/03081088308817561 | MR 0718953 | Zbl 0525.15006
[8] Koliha, J. J., Djordjević, D., Cvetković, D.: Moore-Penrose inverse in rings with involution. Linear Algebra Appl. 426 (2007), 371-381. DOI 10.1016/j.laa.2007.05.012 | MR 2350664 | Zbl 1130.46032
[9] Mosić, D., Djordjević, D. S.: Moore-Penrose-invertible normal and Hermitian elements in rings. Linear Algebra Appl. 431 (2009), 732-745. DOI 10.1016/j.laa.2009.03.023 | MR 2535546 | Zbl 1186.16046
[10] Mosić, D., Djordjević, D. S.: Partial isometries and EP elements in rings with involution. Electron. J. Linear Algebra 18 (2009), 761-772. DOI 10.13001/1081-3810.1343 | MR 2578068 | Zbl 1192.16039
[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. DOI 10.1016/j.mcm.2011.02.035 | MR 2801901 | Zbl 1225.15008
[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. DOI 10.1016/j.amc.2011.12.030 | MR 2880325 | Zbl 1251.15008
[13] Mosić, D., Djordjević, D. S., Koliha, J. J.: EP elements in rings. Linear Algebra Appl. 431 (2009), 527-535. DOI 10.1016/j.laa.2009.02.032 | MR 2535530 | Zbl 1186.16047
[14] Penrose, R.: A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51 (1955), 406-413. DOI 10.1017/S0305004100030401 | MR 0069793 | Zbl 0065.24603
[15] Xu, S., Chen, J., Benítez, J.: EP elements in rings with involution. Available at https://arxiv.org/abs/1602.08184 (2017), 18 pages.
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