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Title: Explicit solutions of infinite linear systems associated with group inverse endomorphisms (English)
Author: Pablos Romo, Fernando
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 72
Issue: 3
Year: 2022
Pages: 751-763
Summary lang: English
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Category: math
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Summary: The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As particular results, we provide different properties of the group inverse and we characterize EP endomorphisms of arbitrary vector spaces from the coincidence of the group inverse and the Moore-Penrose inverse.\looseness -1 (English)
Keyword: infinite linear system
Keyword: group inverse
Keyword: Moore-Penrose inverse
Keyword: EP endomorphism
MSC: 15A04
MSC: 15A06
MSC: 15A09
idZBL: Zbl 07584100
idMR: MR4467940
DOI: 10.21136/CMJ.2022.0143-21
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Date available: 2022-08-22T08:21:43Z
Last updated: 2024-10-04
Stable URL: http://hdl.handle.net/10338.dmlcz/150615
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Reference: [1] Sánchez, V. Cabezas, Romo, F. Pablos: Explicit solutions of infinite systems of linear equations from reflexive generalized inverses of finite potent endomorphisms.Linear Algebra Appl. 559 (2018), 125-144. Zbl 1403.15002, MR 3857542, 10.1016/j.laa.2018.09.004
Reference: [2] Sánchez, V. Cabezas, Romo, F. Pablos: Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces.Electron. J. Linear Algebra 36 (2020), 570-586. Zbl 1451.15003, MR 4148552, 10.13001/ela.2020.4979
Reference: [3] S. L. Campbell, C. D. Meyer, Jr.: Generalized Inverses of Linear Transformations.Classics in Applied Mathematics 56. SIAM, Philadelphia (2009). Zbl 1158.15301, MR 3396208, 10.1137/1.9780898719048
Reference: [4] Cheng, S., Tian, Y.: Two sets of new characterizations for normal and EP matrices.Linear Algebra Appl. 375 (2003), 181-195. Zbl 1054.15022, MR 2013464, 10.1016/S0024-3795(03)00650-5
Reference: [5] Drazin, M. P.: Pseudo-inverses in associative rings and semigroups.Am. Math. Mon. 65 (1958), 506-514. Zbl 0083.02901, MR 0098762, 10.2307/2308576
Reference: [6] Romo, F. Pablos: Group inverse of finite potent endomorphisms on arbitrary vector spaces.Oper. Matrices 14 (2020), 1029-1042. Zbl 07446808, MR 4207170, 10.7153/oam-2020-14-64
Reference: [7] Robert, P.: On the group-inverse of a linear transformation.J. Math. Anal. Appl. 22 (1968), 658-669. Zbl 0159.32101, MR 0229658, 10.1016/0022-247X(68)90204-7
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