The \(\mathfrak{m}\)-core-EP inverse in Minkowski space. (English) Zbl 1498.15005
Summary: In this paper, we introduce the \(\mathfrak{m}\)-core-EP inverse in Minkowski space, consider its properties, and get several sufficient and necessary conditions for the existence of the \(\mathfrak{m}\)-core-EP inverse. We give the \(\mathfrak{m}\)-core-EP decomposition in Minkowski space, and note that not every square matrix has the decomposition. Furthermore, by applying the \(\mathfrak{m}\)-core-EP inverse and the \(\mathfrak{m}\)-core-EP decomposition, we introduce the \(\mathfrak{m}\)-core-EP order and give some characterizations of it.
MSC:
| 15A09 | Theory of matrix inversion and generalized inverses |
| 15A10 | Applications of generalized inverses |
| 15A24 | Matrix equations and identities |
References:
| [1] | Ben-Israel, A.; Greville, TNE, Generalized Inverses: Theory and Applications (2003), New York: Springer, New York · Zbl 1026.15004 |
| [2] | Ferreyra, DE; Levis, FE; Thome, N., Revisiting the core-EP inverse and its extension to rectangular matrices, Quaest. Math., 41, 265-281 (2018) · Zbl 1390.15010 · doi:10.2989/16073606.2017.1377779 |
| [3] | Gao, Y., Perturbation bounds for the W-weighted core-EP inverse, J. Algebra Appl., 19, 2050232 (2020) · Zbl 1454.15005 · doi:10.1142/S0219498820502321 |
| [4] | Gao, Y.; Chen, J., Pseudo core inverses in rings with involution, Commun. Algebra, 46, 38-50 (2018) · Zbl 1392.15005 · doi:10.1080/00927872.2016.1260729 |
| [5] | Ji, J.; Wei, Y., The core-EP, weighted core-EP inverse of matrices, and constrained systems of linear equations, Commun. Math. Res., 37, 86-112 (2021) · Zbl 1513.15005 · doi:10.4208/cmr.2020-0028 |
| [6] | Kılıçman, A.; Al-Zhour, Z., The representation and approximation for the weighted Minkowski inverse in Minkowski space, Math. Comput. Model., 47, 363-371 (2008) · Zbl 1151.15009 · doi:10.1016/j.mcm.2007.03.031 |
| [7] | Ma, H.; Stanimirović, PS, Characterizations, approximation and perturbations of the core-EP inverse, Appl. Math. Comput., 359, 404-417 (2019) · Zbl 1428.15004 |
| [8] | Meenakshi, AR, Generalized inverses of matrices in Minkowski space, Proc. Natl. Semin. Algebra Appl., 57, 1-14 (2000) |
| [9] | Mosić, D., Weighted core-EP inverse of an operator between Hilbert spaces, Linear Multilinear Algebra, 67, 278-298 (2019) · Zbl 07001303 · doi:10.1080/03081087.2017.1418824 |
| [10] | Mosić, D.; Stanimirović, PS; Ma, H., Generalization of core-EP inverse for rectangular matrices, J. Math. Anal. Appl., 500, 125101 (2021) · Zbl 1470.15006 · doi:10.1016/j.jmaa.2021.125101 |
| [11] | Mosić, D.; Stanimirović, PS; Katsikis, VN, Computational and applied mathematics solvability of some constrained matrix approximation problems using core-EP inverses, Comput. Appl. Math., 39, 311 (2020) · Zbl 1476.15006 · doi:10.1007/s40314-020-01360-y |
| [12] | Petrović, M.; Stanimirović, PS, Representations and computations of \(\{2, 3^~\}\) and \(\{2, 4^~\}\)-inverses in indefinite inner product spaces, Appl. Math. Comput., 254, 157-171 (2015) · Zbl 1410.15012 |
| [13] | Prasad, KM; Mohana, KS, Core-EP inverse, Linear Multilinear Algebra, 62, 792-802 (2014) · Zbl 1306.15006 · doi:10.1080/03081087.2013.791690 |
| [14] | Renardy, M., Singular value decomposition in Minkowski space, Linear Algebra Appl., 236, 53-58 (1996) · Zbl 0846.15008 · doi:10.1016/0024-3795(94)00124-3 |
| [15] | Sahoo, JK; Behera, R.; Stanimirović, PS; Katsikis, VN; Ma, H., Core and core-EP inverses of tensors, Comput. Appl. Math., 39, 168-187 (2020) · Zbl 1449.15061 |
| [16] | Wang, G.; Wei, Y.; Qiao, S., Generalized Inverses: Theory and Computations (2018), Beijing: Science Press, Beijing · Zbl 1395.15002 · doi:10.1007/978-981-13-0146-9 |
| [17] | Wang, H., Core-EP decomposition and its applications, Linear Algebra Appl., 508, 289-300 (2016) · Zbl 1346.15003 · doi:10.1016/j.laa.2016.08.008 |
| [18] | Wang, H., Li, N., Liu, X.: The \({{\mathfrak{m}}} \)-core inverse and its applications. Linear Multilinear Algebra 69, 2491-2509 (2021) · Zbl 1473.15011 |
| [19] | Zhou, M.; Chen, J.; Li, T.; Wang, D., Three limit representations of the core-EP inverse, Filomat, 32, 5887-5894 (2018) · Zbl 1499.15020 · doi:10.2298/FIL1817887Z |
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