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Original Articles

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

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Pages 547-559 | Received 20 Aug 2007, Accepted 17 Dec 2007, Published online: 13 Jul 2009

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Predrag S. Stanimirović, Vasilios N. Katsikis, Zhijun Zhang, Shuai Li, Jianlong Chen & Mengmeng Zhou. (2020) Varying-parameter Zhang neural network for approximating some expressions involving outer inverses. Optimization Methods and Software 35:6, pages 1304-1330.
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Predrag S. Stanimirović, Dimitrios Pappas, Vasilios N. Katsikis & Marija S. Cvetković. (2015) Outer inverse restricted by a linear system. Linear and Multilinear Algebra 63:12, pages 2461-2493.
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Ivan I. Kyrchei, Dijana Mosić & Predrag S. Stanimirović. 2023. Matrix and Operator Equations and Applications. Matrix and Operator Equations and Applications 73 138 .
Predrag S. Stanimirović, Vasilios N. Katsikis, Long Jin & Dijana Mosić. (2021) Properties and computation of continuous-time solutions to linear systems. Applied Mathematics and Computation 405, pages 126242.
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Ivan I. Kyrchei, Dijana Mosić & Predrag Stanimirović. (2021) MPD-DMP-solutions to quaternion two-sided restricted matrix equations. Computational and Applied Mathematics 40:5.
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Jie Ma, Feng Gao & Yongshu Li. (2019) An efficient method for computing the outer inverse $A_{T,S}^{(2)}$ through Gauss-Jordan elimination. Numerical Algorithms 85:1, pages 77-106.
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Ivan I. Kyrchei. (2020) Determinantal Representations of the Weighted Core-EP, DMP, MPD, and CMP Inverses. Journal of Mathematics 2020, pages 1-12.
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Xingping Sheng. (2020) Two closed novel formulas for the generalized inverse A T , S (2) of a complex matrix with given rank . Journal of Inverse and Ill-posed Problems 28:1, pages 33-42.
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Guang-Jing Song, Qing-Wen Wang & Shao-Wen Yu. (2018) Cramer’s rule for a system of quaternion matrix equations with applications. Applied Mathematics and Computation 336, pages 490-499.
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Xue-Zhong Wang, Predrag S. Stanimirović & Yimin Wei. (2018) Complex ZFs for computing time-varying complex outer inverses. Neurocomputing 275, pages 983-1001.
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Ravindra B. Bapat, Manjunatha Prasad Karantha, Nupur Nandini & Divya P. Shenoy. (2018) Outer inverses and Jacobi type identities. Linear Algebra and its Applications 536, pages 274-294.
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Guang-Jing Song & Chang-Zhou Dong. (2015) New results on condensed Cramer’s rule for the general solution to some restricted quaternion matrix equations. Journal of Applied Mathematics and Computing 53:1-2, pages 321-341.
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Guang-Jing Song, Haixia Chang & Zhongcheng Wu. (2014) Cramer’s rules for various solutions to some restricted quaternionic linear systems. Journal of Applied Mathematics and Computing 48:1-2, pages 83-109.
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Shwetabh Srivastava & Dharmendra K. Gupta. (2014) A new representation for . Applied Mathematics and Computation 243, pages 514-521.
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Guang-Jing Song & Shaowen Yu. (2014) The block independence in the generalized inverse for some ordered matrices and applications . Applied Mathematics and Computation 232, pages 399-410.
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Yimin Wei. 2013. Handbook of Linear Algebra, Second Edition. Handbook of Linear Algebra, Second Edition 445 469 .
Xingping Sheng & Guoliang Chen. (2013) Innovation based on Gaussian elimination to compute generalized inverse . Computers & Mathematics with Applications 65:11, pages 1823-1829.
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Predrag S. Stanimirović & Milan Lj. Zlatanović. (2012) Determinantal Representation of Outer Inverses in Riemannian Space. Algebra Colloquium 19:spec01, pages 877-892.
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Guang-Jing Song. (2012) Determinantal representation of the generalized inverses over the quaternion skew field with applications. Applied Mathematics and Computation 219:2, pages 656-667.
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Guang-Jing Song. (2011) Determinantal representations of the generalized inverses $A_{T,S}^{(2)}$ over the quaternion skew field with applications. Journal of Applied Mathematics and Computing 39:1-2, pages 201-220.
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Xiaoji Liu, Guangyan Zhu, Guangping Zhou & Yaoming Yu. (2012) An Analog of the Adjugate Matrix for the Outer Inverse . Mathematical Problems in Engineering 2012, pages 1-14.
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Marko Miladinović, Sladjana Miljković & Predrag Stanimirović. (2011) Modified SMS method for computing outer inverses of Toeplitz matrices. Applied Mathematics and Computation 218:7, pages 3131-3143.
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Guang-Jing Song & Qing-Wen Wang. (2011) Condensed Cramer rule for some restricted quaternion linear equations. Applied Mathematics and Computation 218:7, pages 3110-3121.
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Hongxing Wang, Musheng Wei & Xiaoji Liu. (2011) Several Representations of {2}-Inverses. Arabian Journal for Science and Engineering 36:6, pages 1161-1169.
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Guang-Jing Song, Qing-Wen Wang & Hai-Xia Chang. (2011) Cramer rule for the unique solution of restricted matrix equations over the quaternion skew field. Computers & Mathematics with Applications 61:6, pages 1576-1589.
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Xingping Sheng & Guoliang Chen. (2011) New proofs of two representations and minor of generalized inverse . Applied Mathematics and Computation 217:13, pages 6309-6314.
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Xiaoji Liu & Jin Zhong. (2010) Integral representation of the W-weighted Drazin inverse for Hilbert space operators. Applied Mathematics and Computation 216:11, pages 3228-3233.
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Xiaoji Liu, Chunmei Hu & Yaoming Yu. (2010) Further results on iterative methods for computing generalized inverses. Journal of Computational and Applied Mathematics 234:3, pages 684-694.
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Dijana Mosić & Dragan S. Djordjević. (2009) Condition number related to the outer inverse of a complex matrix. Applied Mathematics and Computation 215:8, pages 2826-2834.
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Xiaoji Liu, Yaoming Yu & Chunmei Hu. (2009) The iterative methods for computing the generalized inverse of the bounded linear operator between Banach spaces. Applied Mathematics and Computation 214:2, pages 391-410.
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Dragana Cvetkovic ILic, Xiaoji Liu & Jin Zhong. (2009) On the outer generalized inverse in Banach algebra. Applied Mathematics and Computation 209:2, pages 191-196.
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Xiaoji Liu, Yaoming Yu & Hongxing Wang. (2009) Determinantal representation of weighted generalized inverses. Applied Mathematics and Computation 208:2, pages 556-563.
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