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Weighted binary relations involving the Drazin inverse

Author

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  • Hernández, A.
  • Lattanzi, M.
  • Thome, N.

Abstract

The Drazin inverse of a matrix has been used in the literature to define a pre-order on the set of square complex matrices. In this paper we analyze new binary relations defined on the set of rectangular complex matrices and some relationships to the W-support idempotent. We introduce the class of weighted Drazin equal projectors and analyze the pre-orders on this class. Moreover, adjacent matrices are studied under the considered relations. Finally, some observations on weighted partial orders are given.

Suggested Citation

  • Hernández, A. & Lattanzi, M. & Thome, N., 2015. "Weighted binary relations involving the Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 215-223.
    • Handle: RePEc:eee:apmaco:v:253:y:2015:i:c:p:215-223
    DOI: 10.1016/j.amc.2014.12.102
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    References listed on IDEAS

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    1. Baksalary, Jerzy K. & Hauke, Jan, 1984. "Inheriting independence and chi-squaredness under certain matrix orderings," Statistics & Probability Letters, Elsevier, vol. 2(1), pages 35-38, January.
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    Cited by:

    1. Hernández, A. & Lattanzi, M. & Thome, N., 2016. "On some new pre-orders defined by weighted Drazin inverses," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 108-116.
    2. Mosić, Dijana & Djordjević, Dragan S., 2015. "Weighted pre-orders involving the generalized Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 496-504.
    3. Coll, C. & Lattanzi, M. & Thome, N., 2018. "Weighted G-Drazin inverses and a new pre-order on rectangular matrices," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 12-24.
    4. Mosić, Dijana, 2016. "Reverse order laws for the generalized strong Drazin inverses," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 37-46.
    5. Deng, Chunyuan & Yu, Anqi, 2015. "Relationships between DMP relation and some partial orders," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 41-53.
    6. Wang, Xue-Zhong & Ma, Haifeng & Stanimirović, Predrag S., 2017. "Recurrent neural network for computing the W-weighted Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 1-20.

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    1. Mosić, Dijana & Djordjević, Dragan S., 2015. "Weighted pre-orders involving the generalized Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 496-504.

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