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Analogs of the adjoint matrix for generalized inverses and corresponding Cramer rules. (English) Zbl 1141.15005

The author introduces determinantal representations of the Moore-Penrose inverse and the Drazin inverse. Cramer rules for the least squares solution and for the Drazin inverse solution of singular linear systems are also given by using the obtained results.

MSC:

15A09 Theory of matrix inversion and generalized inverses
15B57 Hermitian, skew-Hermitian, and related matrices
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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: 10.1017/S0305004100066172 · Zbl 0616.15003 · doi:10.1017/S0305004100066172
[3] DOI: 10.1016/0024-3795(82)90255-5 · Zbl 0487.15004 · doi:10.1016/0024-3795(82)90255-5
[4] Campbell SL, Generalized Inverse of Linear Transformations (1979)
[5] Carl D, SIAM Journal on Applied Mathematics 26 pp 506– (1974)
[6] DOI: 10.1080/03081089308818219 · Zbl 0796.15005 · doi:10.1080/03081089308818219
[7] DOI: 10.2307/2308576 · Zbl 0083.02901 · doi:10.2307/2308576
[8] Gabriel R, Journal für die Reine Angewandte Mathematik 234 pp 107– (1967)
[9] Horn RA, The Matrix Analysis (1985) · Zbl 0576.15001 · doi:10.1017/CBO9780511810817
[10] DOI: 10.1016/j.laa.2005.02.025 · Zbl 1078.15004 · doi:10.1016/j.laa.2005.02.025
[11] Moore EH, Bulletin of the American Mathematical Society 26 pp 394– (1920)
[12] Stanimirovic’ PS, Matematichki Vesnik 48 pp 1– (1996)
[13] DOI: 10.1016/S0024-3795(00)00075-6 · Zbl 0956.15005 · doi:10.1016/S0024-3795(00)00075-6
[14] DOI: 10.1016/0024-3795(86)90123-0 · Zbl 0588.15005 · doi:10.1016/0024-3795(86)90123-0
[15] DOI: 10.1016/0024-3795(89)90395-9 · Zbl 0671.15006 · doi:10.1016/0024-3795(89)90395-9
[16] Wei YM, The Electronic Journal of Linear Algebra 8 pp 83– (2001) · Zbl 1051.65053 · doi:10.1002/1099-1506(200103)8:2<83::AID-NLA231>3.0.CO;2-X
[17] DOI: 10.1080/03081088408817600 · Zbl 0544.15002 · doi:10.1080/03081088408817600
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