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Determinantal representation of the generalized inverse \(A_{T,S}^{(2)}\) over integral domains and its applications. (English) Zbl 1182.15007

Determinantal representations of \(\{1,5\}\)-inverses and \(A^{(2)}_{T,S}\) generalized inverses over an integral domain are given. In addition, the determinantal representation of solutions of restricted linear equations over the complex field is studied as an application.

MSC:

15A09 Theory of matrix inversion and generalized inverses
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A06 Linear equations (linear algebraic aspects)
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[1] DOI: 10.1016/0024-3795(90)90229-6 · Zbl 0712.15004 · doi:10.1016/0024-3795(90)90229-6
[2] DOI: 10.1016/0024-3795(92)90340-G · Zbl 0762.15003 · doi:10.1016/0024-3795(92)90340-G
[3] Ben-Israel A, Generalized Inverses: Theory and Applications, 2. ed. (2003)
[4] DOI: 10.1016/0024-3795(86)90307-1 · Zbl 0562.15003 · doi:10.1016/0024-3795(86)90307-1
[5] DOI: 10.1016/0024-3795(83)90102-7 · Zbl 0505.15002 · doi:10.1016/0024-3795(83)90102-7
[6] Bhaskara Rao KPS, The Theory of Generalized Inverses over Commutative Rings, Algebra, Logic and Applications Series 17 (2002)
[7] DOI: 10.1002/nla.513 · Zbl 1199.15016 · doi:10.1002/nla.513
[8] DOI: 10.1080/03081089308818219 · Zbl 0796.15005 · doi:10.1080/03081089308818219
[9] DOI: 10.1080/03081089508818420 · Zbl 0855.65034 · doi:10.1080/03081089508818420
[10] DOI: 10.2307/2282625 · Zbl 0144.42401 · doi:10.2307/2282625
[11] DOI: 10.1016/0024-3795(80)90230-X · Zbl 0433.15002 · doi:10.1016/0024-3795(80)90230-X
[12] Cui, X and Wei, Y. 2007. ”Determinantal representation of the group inverse and the Drazin inverse”. preprint
[13] DOI: 10.1137/S0895479802418860 · Zbl 1097.15006 · doi:10.1137/S0895479802418860
[14] DOI: 10.1080/03081080701352856 · Zbl 1141.15005 · doi:10.1080/03081080701352856
[15] DOI: 10.1016/0024-3795(92)90229-4 · Zbl 0743.15007 · doi:10.1016/0024-3795(92)90229-4
[16] DOI: 10.1016/0024-3795(91)90018-R · Zbl 0722.15007 · doi:10.1016/0024-3795(91)90018-R
[17] DOI: 10.1080/03081089308818251 · Zbl 0787.15006 · doi:10.1080/03081089308818251
[18] DOI: 10.1017/S0305004100030929 · doi:10.1017/S0305004100030929
[19] DOI: 10.1016/S0024-3795(00)00075-6 · Zbl 0956.15005 · doi:10.1016/S0024-3795(00)00075-6
[20] Wang, G, Wei, Y and Qiao, S. 2004. ”Generalized Inverses: Theory and Computations”. Beijing: Science Press. · Zbl 1395.15002
[21] DOI: 10.1016/S0024-3795(98)00008-1 · Zbl 0934.15003 · doi:10.1016/S0024-3795(98)00008-1
[22] DOI: 10.1016/S0096-3003(00)00132-6 · Zbl 1026.15005 · doi:10.1016/S0096-3003(00)00132-6
[23] Yu Y, J. Shanghai Normal Univ., (N.S.) 32 pp 12– (2003)
[24] DOI: 10.1080/03081080500079510 · Zbl 1086.15004 · doi:10.1080/03081080500079510
[25] Yu Y, Aust. J. Math. Appl. 4 pp 1– (2007)
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