Weighted generalized Moore–Penrose inverse

References

[1] R. Behera, G. Maharana and J. K. Sahoo, Further results on weighted core-EP inverse of matrices, Results Math. 75 (2020), no. 4, Paper No. 174. 10.1007/s00025-020-01296-zSearch in Google Scholar

[2] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, 2nd ed., Robert E. Krieger, Huntington, 2003. Search in Google Scholar

[3] Y. Chen, K. Zuo and Z. Fu, New characterizations of the generalized Moore–Penrose inverse of matrices, AIMS Math. 7 (2022), no. 3, 4359–4375. 10.3934/math.2022242Search in Google Scholar

[4] S. Chountasis, V. N. Katsikis and D. Pappas, Applications of the Moore–Penrose inverse in digital image restoration, Math. Probl. Eng. 2009 (2009), Article ID 170724. 10.1155/2009/170724Search in Google Scholar

[5] S. Chountasis, V. N. Katsikis and D. Pappas, Digital image reconstruction in the spectral domain utilizing the Moore–Penrose inverse, Math. Probl. Eng. 2010 (2010), Article ID 750352. 10.1155/2010/750352Search in Google Scholar

[6] R. E. Cline and T. N. E. Greville, A Drazin inverse for rectangular matrices, Linear Algebra Appl. 29 (1980), 53–62. 10.1016/0024-3795(80)90230-XSearch in Google Scholar

[7] C. Coll, M. Lattanzi and N. Thome, Weighted G-Drazin inverses and a new pre-order on rectangular matrices, Appl. Math. Comput. 317 (2018), 12–24. 10.1016/j.amc.2017.08.047Search in Google Scholar

[8] A. Dajić and J. J. Koliha, The weighted g-Drazin inverse for operators, J. Aust. Math. Soc. 82 (2007), no. 2, 163–181. 10.1017/S1446788700016013Search in Google Scholar

[9] C. Y. Deng and H. K. Du, Representations of the Moore-Penrose inverse of 2 × 2 block operator valued matrices, J. Korean Math. Soc. 46 (2009), no. 6, 1139–1150. 10.4134/JKMS.2009.46.6.1139Search in Google Scholar

[10] M. P. Drazin, Pseudo-inverses in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506–514. 10.1080/00029890.1958.11991949Search in Google Scholar

[11] D. E. Ferreyra, F. E. Levis and N. Thome, Revisiting the core EP inverse and its extension to rectangular matrices, Quaest. Math. 41 (2018), no. 2, 265–281. 10.2989/16073606.2017.1377779Search in Google Scholar

[12] Y. Gao and J. Chen, Pseudo core inverses in rings with involution, Comm. Algebra 46 (2018), no. 1, 38–50. 10.1080/00927872.2016.1260729Search in Google Scholar

[13] Y. Gao, J. Chen and P. Patrício, Representations and properties of the W-weighted core-EP inverse, Linear Multilinear Algebra 68 (2020), no. 6, 1160–1174. 10.1080/03081087.2018.1535573Search in Google Scholar

[14] S. Gigola, L. Lebtahi and N. Thome, The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem, J. Comput. Appl. Math. 291 (2016), 449–457. 10.1016/j.cam.2015.03.052Search in Google Scholar

[15] R. Harte, Invertibility and Singularity for Bounded Linear Operators, Monogr. Textb. Pure Appl. Math. 109, Marcel Dekker, New York, 1988. Search in Google Scholar

[16] J. J. Koliha, A generalized Drazin inverse, Glasg. Math. J. 38 (1996), no. 3, 367–381. 10.1017/S0017089500031803Search in Google Scholar

[17] I. Kyrchei, Weighted quaternion core-EP, DMP, MPD, and CMP inverses and their determinantal representations, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (2020), no. 4, Paper No. 198. 10.1007/s13398-020-00930-3Search in Google Scholar

[18] I. I. Kyrchei, D. Mosić and P. S. Stanimirović, Weighted minimization problems for quaternion matrices, Adv. Appl. Clifford Algebr. 31 (2021), no. 3, Paper No. 48. 10.1007/s00006-021-01153-4Search in Google Scholar

[19] L. Lebtahi and N. Thome, A note on k-generalized projections, Linear Algebra Appl. 420 (2007), no. 2–3, 572–575. 10.1016/j.laa.2006.08.011Search in Google Scholar

[20] H. Ma, A characterization and perturbation bounds for the weighted core-EP inverse, Quaest. Math. 43 (2020), no. 7, 869–879. 10.2989/16073606.2019.1584773Search in Google Scholar

[21] H. Ma, P. S. Stanimirović, D. Mosić and I. I. Kyrchei, Sign pattern, usability, representations and perturbation for the core-EP and weighted core-EP inverse, Appl. Math. Comput. 404 (2021), Paper No. 126247. 10.1016/j.amc.2021.126247Search in Google Scholar

[22] S. B. Malik and N. Thome, On a revisited Moore-Penrose inverse of a linear operator on Hilbert spaces, Filomat 31 (2017), no. 7, 1927–1931. 10.2298/FIL1707927MSearch in Google Scholar

[23] K. Manjunatha Prasad and K. S. Mohana, Core-EP inverse, Linear Multilinear Algebra 62 (2014), no. 6, 792–802. 10.1080/03081087.2013.791690Search in Google Scholar

[24] D. Mosić, Weighted GDMP inverse of operators between Hilbert spaces, Bull. Korean Math. Soc. 55 (2018), no. 4, 1263–1271. Search in Google Scholar

[25] D. Mosić, Weighted core-EP inverse of an operator between Hilbert spaces, Linear Multilinear Algebra 67 (2019), no. 2, 278–298. 10.1080/03081087.2017.1418824Search in Google Scholar

[26] D. Mosić, Maximal classes of operators determining some weighted generalized inverses, Linear Multilinear Algebra 68 (2020), no. 11, 2201–2220. 10.1080/03081087.2019.1575328Search in Google Scholar

[27] D. Mosić, Perturbation of the weighted core-EP inverse, Ann. Funct. Anal. 11 (2020), no. 1, 75–86. 10.1007/s43034-019-00022-3Search in Google Scholar

[28] D. Mosić and D. S. Djordjević, The gDMP inverse of Hilbert space operators, J. Spectr. Theory 8 (2018), no. 2, 555–573. 10.4171/JST/207Search in Google Scholar

[29] D. Mosić and M. Z. Kolundžija, Weighted CMP inverse of an operator between Hilbert spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 3, 2155–2173. 10.1007/s13398-018-0603-zSearch in Google Scholar

[30] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406–413. 10.1017/S0305004100030401Search in Google Scholar

[31] K. S. Stojanović and D. Mosić, Generalization of the Moore-Penrose inverse, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (2020), no. 4, Paper No. 196. 10.1007/s13398-020-00928-xSearch in Google Scholar