Explicit formulae for the Drazin inverse of the sum of two matrices

References

[1] Abdolyousefi, M. S.: The representations of the g-Drazin inverse in a Banach algebra, Hacet. J. Math. Stat. 50 (2021), 659–667.10.15672/hujms.754006Suche in Google Scholar

[2] Behera, R.—Nandi, A. K.—Sahoo, J. K.: Further results on the Drazin inverse of even-order tensors, Numer. Linear Algebra Appl. 27 (2020), e2317.10.1002/nla.2317Suche in Google Scholar

[3] Benítez, J.—Liu, X.—Qin, Y.: Representations for the generalized Drazin inverse in a Banach algebra, Bull. Math. Anal. Appl. 5 (2013), 53–64.Suche in Google Scholar

[4] Bu, C.—Feng, C.—Bai, S.: Representations for the Drazin inverses of the sum of two matrices and some block matrices, Appl. Math. Comput. 218 (2012), 10226–10237.10.1016/j.amc.2012.03.102Suche in Google Scholar

[5] Campbell, S. L.: The Drazin inverse and systems of second order linear differential equations, Linear Multilinear Algebra 14 (1983), 195–198.10.1080/03081088308817556Suche in Google Scholar

[6] Campbell, S. L.—Meyer, C. D.—Rose, N. J.: Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM J. Appl. Math. 31 (1976), 411–425.10.1137/0131035Suche in Google Scholar

[7] Castro-González, N.—Dopazo, E.—Martínez-Serrano, M. F.: On the Drazin inverse of the sum of two operators and its application to operator matrices, J. Math. Anal. Appl. 350 (2008), 207–215.10.1016/j.jmaa.2008.09.035Suche in Google Scholar

[8] Catral, M.—Olesky, D. D.—van den Driessche, P.: Block representations of the Drazin inverse of a bipartite matrix, Electron. J. Linear Algebra 18 (2009), 98–107.10.13001/1081-3810.1297Suche in Google Scholar

[9] Cline, R. E.: An application of representation for the generalized inverse of a matrix, MRC Technical Report 592 (1965).Suche in Google Scholar

[10] Cvetković-Ilić, D. S.: A note on the representation for the Drazin inverse of 2×2 block matrices, Linear Algebra Appl. 429 (2008), 242–248.10.1016/j.laa.2008.02.019Suche in Google Scholar

[11] Cvetković-Ilić, D. S.: New additive results on Drazin inverse and its applications, Appl. Math. Comput. 218 (2011), 3019–3024.10.1016/j.amc.2011.08.083Suche in Google Scholar

[12] Cvetković-Ilić, D. S.—Chen, J.—Xu, Z.: Explicit representations of the Drazin inverse of block matrix and modified matrix, Linear Multilinear Algebra 14 (2008), 1–10.Suche in Google Scholar

[13] Djordjević, D. S.—Stanimirović, P. S.: On the generalized Drazin inverse and generalized resolvent, Czechoslovak Math. J. 51 (2001), 617–634.10.1023/A:1013792207970Suche in Google Scholar

[14] Dopazo, E.—Martínez-Serrano, M. F.: Further results on the representation of the Drazin inverse of a 2 × 2 block matrix, Linear Algebra Appl. 432 (2010), 1896–1904.10.1016/j.laa.2009.02.001Suche in Google Scholar

[15] Dopazo, E.—Martínez-Serrano, M. F.—Robles, J.: Block representations for the Drazin inverse of anti-triangular matrices, Filomat 30 (2016), 3897–3906.10.2298/FIL1614897DSuche in Google Scholar

[16] Drazin, M. P.: Pseudoinverses in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506–514.10.1080/00029890.1958.11991949Suche in Google Scholar

[17] Hartwig, R. E.—Li, X.—Wei, Y.: Representations for the Drazin inverse of a 2 × 2 block matrix, SIAM J. Matrix Anal. Appl. 27 (2006), 757–771.10.1137/040606685Suche in Google Scholar

[18] Hartwig, R. E.—Shoaf, J. M.: Group inverses and Drazin inverses of bidiagonal and triangular Toeplitz matrices, J. Aust. Math. Soc. 24 (1977), 10–34.10.1017/S1446788700020036Suche in Google Scholar

[19] Hartwig, R. E.—Wang, G.— Wei, Y.: Some additive results on Drazin inverse, Linear Algebra Appl. 322 (2001), 207–217.10.1016/S0024-3795(00)00257-3Suche in Google Scholar

[20] Kyrchei, I.: Explicit formulas for determinantal representations of the Drazin inverse solutions of some matrix and differential matrix equations, Appl. Math. Comput. 219 (2013), 7632–7644.10.1016/j.amc.2013.01.050Suche in Google Scholar

[21] Kyrchei, I.: Determinantal representations of the Drazin inverse over the quaternion skew field with applications to some matrix equations, Appl. Math. Comput. 238 (2014), 193–207.10.1016/j.amc.2014.03.125Suche in Google Scholar

[22] Ljubisavljević, J.—Cvetković-Ilić, D. S.: Representations for Drazin inverse of block matrix, J. Comput. Anal. Appl. 15 (2013), 481–497.Suche in Google Scholar

[23] Meyer, C. D.: The role of the group generalized inverse in the theory of finite Markov chains, SIAM Rev. 17 (1975), 443–464.10.1137/1017044Suche in Google Scholar

[24] Meyer, C. D.: The condition number of a finite Markov chains and perturbation bounds for the limitimg probabilities, SIAM J. Alg. Dis. Methods 1 (1980), 273–283.10.1137/0601031Suche in Google Scholar

[25] Meyer, C. D.—Plemmons, R. J.: Convergent powers of a matrix with applications to iterative methods for singular systems of linear systems, SIAM J. Numer. Anal. 14 (1977), 699–705.10.1137/0714047Suche in Google Scholar

[26] Meyer, C. D.—Rose, N. J.: The index and the Drazin inverse of block triangular matrices, SIAM J. Appl. Math. 33 (1977), 1–7.10.1137/0133001Suche in Google Scholar

[27] Mosić, D.: The Drazin inverse of the sum of two matrices, Math. Slovaca 68 (2018), 767–772.10.1515/ms-2017-0143Suche in Google Scholar

[28] Robles, J.—Martínez-Serrano, M. F.—Dopazo, E.: On the generalized Drazin inverse in Banach algebras in terms of the generalized Schur complement, Appl. Math. Comput. 284 (2016), 162–168.10.1016/j.amc.2016.02.057Suche in Google Scholar

[29] Sendra, J. R.—Sendra, J.: Symbolic computation of Drazin inverses by specializations, J. Comput. Anal. Appl. 301 (2016), 201–212.10.1016/j.cam.2016.01.059Suche in Google Scholar

[30] Sohrabi, M.: Relationship between Cauchy dual and Drazin inverse of conditional type operators, Bull. Sci. Math. 176 (2022), Art. ID 103119.10.1016/j.bulsci.2022.103119Suche in Google Scholar

[31] Stanimirović, P. S.—Pappas, D.—Katsikis, V. N.—Stanimirović, I. P.: Full-rank representations of outer inverses based on the QR decomposition, Appl. Math. Comput. 218 (2012), 10321–10333.10.1016/j.amc.2012.04.011Suche in Google Scholar

[32] Stanimirović, P. S.—Petković, M. D.—Gerontitis, D.: Gradient neural network with nonlinear activation for computing inner inverses and the Drazin inverse, Neural Process. Lett. 48 (2018), 109–133.10.1007/s11063-017-9705-4Suche in Google Scholar

[33] Yang, H.—Liu, X.: The Drazin inverse of the sum of two matrices and its applications, J. Comput. Appl. Math. 235 (2011), 1412–1417.10.1016/j.cam.2010.08.027Suche in Google Scholar

[34] Yang, X.—Liu, X.—Chen, F.: Some additive results for the Drazin inverse and its application, Filomat 31 (2017), 6493–6500.10.2298/FIL1720493YSuche in Google Scholar

[35] Zhang, D.—Mosić, D.—Stanimirović, P. S.: A formulae for anti-triangular block matrices which include the Drazin inverse, Appl. Anal. Discrete Math. (2024), https://doi.org/10.2298/AADM230418022Z.10.2298/AADM230418022ZSuche in Google Scholar

[36] Zhang, D.— Mosić, D.—Tam, T.: On the existence of group inverses of Peirce corner matrices, Linear Algebra Appl. 582 (2019), 482–498.10.1016/j.laa.2019.07.033Suche in Google Scholar

[37] Zhang, D.—Jin, Y.—Mosić, D.: The Drazin inverse of anti-triangular block matrices, J. Appl. Math. Comput. 68 (2022), 2699–2716.10.1007/s12190-021-01638-2Suche in Google Scholar

[38] Zhang, D.—Jin, Y.—Mosić, D.: A note on formulae for the generalized Drazin inverse of anti-triangular block operator matrices in Banach spaces, Banach J. Math. Anal. 16 (2022), Art. No. 28.10.1007/s43037-022-00176-8Suche in Google Scholar

[39] Zhang, D.—Zhao, Y.—Mosić, D.—Katsikis, V. N.: Exact expressions for the Drazin inverse of anti-triangular matrices, J. Comput. Appl. Math. 428 (2023), Art. ID 115187.10.1016/j.cam.2023.115187Suche in Google Scholar