Advanced Search
Article Contents
Article Contents
Early Access

Early Access articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Early Access publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Early Access articles via the “Early Access” tab for the selected journal.

Drazin theta and theta Drazin matrices

Abstract Full Text(HTML) Related Papers Cited by
  • In this paper, two new classes of matrices - Drazin - theta matrix and theta - Drazin matrix are introduced for a square matrix of index $ m $. Whenever the index is equal to one, we get special case of matrices called Group - theta matrix and theta - Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin -theta and theta - Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin - theta matrix, general solutions of certain types of matrix equations are characterized here.

    Mathematics Subject Classification: Primary: 15A09, 15A24; Secondary: 65F05.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] A. Ben-Israel and  T. N. E GrevilleGeneralized Inverses:Theory and Applications, Springer, Berlin, 2003. 
    [2] C. N. GonzalezJ. J. Koliha and Y. Wei, Integral representation of the Drazin inverse, Electron. J. of Linear Algebra, 9 (2002), 129-131.  doi: 10.13001/1081-3810.1080.
    [3] I. I. Kyrchei, D. Mosić and P. S. Stanimirović, MPD-DMP-solutions to quaternion two-sided restricted matrix equations, Comp. Appl. Math., 40 (2021), Paper No. 177. doi: 10.1007/s40314-021-01566-8.
    [4] A. Lee, Secondary symmetric, skew symmetric and orthogonal matrices, Period. Math. Hung., 7 (1976), 63-70.  doi: 10.1007/BF02019995.
    [5] X. Liu and N. Cai, High-order iterative methods for the DMP inverse, Journal of Mathematics, Article ID 8175935, 2016. doi: 10.1155/2018/8175935.
    [6] H. Ma, X. Gao and P. S. Stanimirović, Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications, Appl. Math. Comput., 378 (2020), Article ID 125196. doi: 10.1016/j.amc.2020.125196.
    [7] H. Ma, Characterizations and representations for the CMP inverse and its application, Linear and Multilinear Algebra, (2021), 1-6. 
    [8] S. B. Malik and N. Thome, On a new generalized inverse for matrices of an arbitrary index, Appl. Math. Comput., 226 (2014), 575-580.  doi: 10.1016/j.amc.2013.10.060.
    [9] M. Mehdipour and A. Salemi, On a new generalized inverse of matrices, Linear and Multilinear Algebra, 66 (2018), 1046-1053.  doi: 10.1080/03081087.2017.1336200.
    [10] C. D. Meyer, Limits and the index of a square matrix, SIAM Journal of Applied Mathematics, 26 (1974), 469-478.  doi: 10.1137/0126044.
    [11] D. Mosić, Drazin-Star and Star-Drazin matrices, Results Math., 75 (2020), 1-21.  doi: 10.1007/s00025-020-01191-7.
    [12] D. MosićP. S. Stanimirović and V. N. Katsikis, Properties of the CMP inverse and its computation, Comp. Appl. Math., 41 (2022), 131.  doi: 10.1007/s40314-022-01847-w.
    [13] C. R. Rao and  S. K. MitraGeneralized Inverse of Matrices and its Applications, Wiley, USA, 1972. 
    [14] A. R. Rao and  P. BhimashankaramLinear Algebra, Tata McGraw - Hill Publishing Company Limited, New Delhi, 1992. 
    [15] P. S. Stanimirović, D. Mosić and Y. Wei, Generalizations of composite inverses with certain image and/or kernel, Appl. Math. Comput., 428 (2022), Article ID 127155. doi: 10.1016/j.amc.2022.127155.
    [16] P. S. StanimirovićD. Mosić and H. Ma, New classes of more general weighted outer inverses, Linear Multilinear Algebra, 70 (2022), 122-147.  doi: 10.1080/03081087.2020.1713712.
    [17] R. Vijayakumar, S-g inverse of s-normal matrices, International Journal of Mathematics Trends and Technology, 4 (2016), 240-244. 
    [18] Y. WeiP.S. Stanimirović and  M. PetkovićNumerical and Symbolic Computations of Generalized Inverses, World Scientific, Hackensack, NJ, 2018. 
    [19] M. ZhouJ. Chen and N. Thome, The W-weighted Drazin-star matrix and its dual, The Electronic Journal of Linear Algebra, 37 (2021), 72-87. 
    [20] K. ZuoD. C. Llic and Y. Cheng, Different characterization of DMP inverse of matrices, Linear and Multilinear Algebra, (2020), 1-8. 
  • 加载中

Article Metrics

HTML views(64) PDF downloads(88) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint