Geodesic
Characterizations of partial isometries and two special kinds of EP elements
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 539-551
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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.
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.
DOI : 10.21136/CMJ.2019.0389-18
Classification : 15A09, 16U99, 16W10
Keywords: EP element; partial isometry; normal EP element; strongly EP element; solutions of equation 
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Zhao, Ruju; Yao, Hua; Wei, Junchao. Characterizations of partial isometries and two special kinds of EP elements. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 539-551. doi: 10.21136/CMJ.2019.0389-18

[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 | MR | JFM

[2] Baksalary, O. M., Trenkler, G.: Characterizations of EP, normal, and Hermitian matrices. Linear Multilinear Algebra 56 (2008), 299-304. | DOI | MR | JFM

[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 | MR | JFM

[4] Chen, W.: On EP elements, normal elements and partial isometries in rings with involution. Electron. J. Linear Algebra 23 (2012), 553-561. | DOI | MR | JFM

[5] Cheng, S., Tian, Y.: Two sets of new characterizations for normal and EP matrices. Linear Algebra Appl. 375 (2003), 181-195. | DOI | MR | JFM

[6] Harte, R., Mbekhta, M.: On generalized inverses in $C^{*}$-algebras. Stud. Math. 103 (1992), 71-77. | DOI | MR | JFM

[7] Hartwig, R. E., Spindelböck, K.: Matrices for which $A^{*}$ and $A^{\dagger}$ commute. Linear Multilinear Algebra 14 (1983), 241-256. | DOI | MR | JFM

[8] Koliha, J. J., Djordjević, D., Cvetković, D.: Moore-Penrose inverse in rings with involution. Linear Algebra Appl. 426 (2007), 371-381. | DOI | MR | JFM

[9] Mosić, D., Djordjević, D. S.: Moore-Penrose-invertible normal and Hermitian elements in rings. Linear Algebra Appl. 431 (2009), 732-745. | DOI | MR | JFM

[10] Mosić, D., Djordjević, D. S.: Partial isometries and EP elements in rings with involution. Electron. J. Linear Algebra 18 (2009), 761-772. | DOI | MR | JFM

[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 | MR | JFM

[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 | MR | JFM

[13] Mosić, D., Djordjević, D. S., Koliha, J. J.: EP elements in rings. Linear Algebra Appl. 431 (2009), 527-535. | DOI | MR | JFM

[14] Penrose, R.: A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51 (1955), 406-413. | DOI | MR | JFM

[15] Xu, S., Chen, J., Benítez, J.: EP elements in rings with involution. Available at , 18 pages. | arXiv

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