| Title:
|
Determinantal representation of $\{I,J,K\}$ inverses and solution of linear systems (English) |
| Author:
|
Stanimirović, Predrag |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
273-286 |
| . |
| Category:
|
math |
| . |
| MSC:
|
15A06 |
| MSC:
|
15A09 |
| MSC:
|
15A15 |
| idZBL:
|
Zbl 0963.15006 |
| idMR:
|
MR1728239 |
| . |
| Date available:
|
2009-09-25T11:37:55Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128881 |
| . |
| Reference:
|
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| Reference:
|
[2] BAPAT R. B.-BHASKARA K. P. S.-MANЈUNATHA PRASAD K.: Generalized inverses over integral domains.Linear Algebra Appl. 140 (1990), 181-196. MR 1075550 |
| Reference:
|
[3] BEN-ISRAEL A.-GREVILE T. N. E.: Generalized Inverses: Theory and Applications.Wileу-Interscience, New York, 1974. Zbl 0305.15001, MR 0396607 |
| Reference:
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[4] BEN-TAL A.: A geometric property of the least squares solution of linear equations.Linear Algebra Appl. 139 (1990), 165-170. Zbl 0704.15005, MR 1071706 |
| Reference:
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[5] BERG L.: Three results in connection with inverse matrices.Linear Algebra Appl. 84 (1986), 63-77. Zbl 0562.15003, MR 0872276 |
| Reference:
|
[6] CLINE R. E.: Inverses of rank invariant powers of a matrix.SIAM Ј. Numer. Anal. 5 (1968), 182-197. Zbl 0165.34602, MR 0227184 |
| Reference:
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[7] ERDELYI I.: On the matrix equation Ax = λBx.Ј. Math. Anal. Appl. 17 (1967), 119-132. MR 0202734 |
| Reference:
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[8] GABRIEL R.: Extinderea complementilor algebrici generalizati la matrici oarecare.Stud. Cerc. Mat. 17 (1965), 1566-1581. MR 0215868 |
| Reference:
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[9] GABRIEL R.: Das verallgemeinerte Inverse einer Matrix über einem beliebigen Körperanalytish betrachtet.J. Reine Angew. Math. 244 (1970), 83-93. MR 0268196 |
| Reference:
|
[10] JOSHI V. N.: A determinant for rectangular matrices.Bull. Australl. Math. Soc. 21 (1980), 137-146. Zbl 0421.15007, MR 0569094 |
| Reference:
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[11] MIAO J.: Reflexive generalized inverses and their minors.Linear and Multilinear Algebra 35 (1993), 153-163. Zbl 0787.15006, MR 1308684 |
| Reference:
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[12] PENROSE R.: A generalized inverse for matrices.Proc. Cambridge Philos. Soc. 51 (1955), 406-413. Zbl 0065.24603, MR 0069793 |
| Reference:
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[13] PRASAD K. M.-BHASKARA RAO K. P. S.-BAPAT R. B.: Generalized inverses over integral domains. II. Group inverses and Drazin inverses.Linear Algebra Appl. 146 (1991), 31-47. MR 1083462 |
| Reference:
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[14] PRASAD K. M.-BAPAT R. B.: The generalized Moore-Penrose inverse.Linear Algebra Appl. 165 (1992), 59-69. Zbl 0743.15007, MR 1149746 |
| Reference:
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[15] PRASAD K. M.: Generalized inverses of matrices over commutative ring.Linear Algebra Appl. 211 (1994), 35-53. MR 1295870 |
| Reference:
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[16] RADIC M.: Some contributions to the inversions of rectangular matrices.Glas. Mat. 1(21) (1966), 23-37. MR 0209301 |
| Reference:
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[17] RADIC M.: A definition of the determinant of a rectangular matrix.Glas. Mat. 1(21) (1966), 17-22. Zbl 0168.02703, MR 0209303 |
| Reference:
|
[18] RAO C. R.-MITRA S. K.: Generalized Inverse of Matrices and its Applications.John Wiley & Sons, Inc, New York-London-Sydney-Toronto, 1971. Zbl 0236.15005, MR 0338013 |
| Reference:
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[19] STANIMIROVIČ P.-STANKOVIČ M.: Determinantal representation of weighted Moore-Penrose inverse.Mat. Vesnik 46 (1994), 41-50. Zbl 0840.15005, MR 1311834 |
| Reference:
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[20] STANIMIROVIČ P.-STANKOVIČ M.: Generalized algebraic complement and Moore-Penrose inverse.Filomat 8 (1994), 57-64. Zbl 0826.15003, MR 1342183 |
| Reference:
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[21] STANIMIROVIČ P.: General determinantal representation of pseudoinverses and its computation.Rev. Acad. Cienc. Zaragoza (2) 50 (1995), 41-49. Zbl 0866.65031, MR 1378381 |
| Reference:
|
[22] STOJAKOVIČ M.: Generalized inverse matrices.In: Mathematical Structures - Computational Mathematics - Mathematical Modelling, Sofia, 1975, pp. 461-470. |
| . |
