| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-08-22T08:21:43Z |
| Last updated:
|
2024-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150615 |
| . |
| 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 |
| . |
