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Explicit solutions of infinite linear systems associated with group inverse endomorphisms. (English) Zbl 07584100

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.

MSC:

15A06 Linear equations (linear algebraic aspects)
15A09 Theory of matrix inversion and generalized inverses
15A04 Linear transformations, semilinear transformations
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[1] Cabezas Sánchez, V.; Pablos Romo, F., Explicit solutions of infinite systems of linear equations from reflexive generalized inverses of finite potent endomorphisms, Linear Algebra Appl., 559, 125-144 (2018) · Zbl 1403.15002
[2] Cabezas Sánchez, V.; Pablos Romo, F., Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces. Electron, J. Linear Algebra, 36, 570-586 (2020) · Zbl 1451.15003
[3] Campbell, S. L.; Meyer, C. D Jr., Generalized Inverses of Linear Transformations (2009), Philadelphia: SIAM, Philadelphia · Zbl 1158.15301
[4] Cheng, S.; Tian, Y., Two sets of new characterizations for normal and EP matrices, Linear Algebra Appl., 375, 181-195 (2003) · Zbl 1054.15022
[5] Drazin, M. P., Pseudo-inverses in associative rings and semigroups, Am. Math. Mon., 65, 506-514 (1958) · Zbl 0083.02901
[6] Pablos Romo, F., Group inverse of finite potent endomorphisms on arbitrary vector spaces, Oper. Matrices, 14, 1029-1042 (2020) · Zbl 1479.15002
[7] Robert, P., On the group-inverse of a linear transformation, J. Math. Anal. Appl., 22, 658-669 (1968) · Zbl 0159.32101
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