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Sign pattern, usability, representations and perturbation for the core-EP and weighted core-EP inverse

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  • Ma, Haifeng
  • Stanimirović, Predrag S.
  • Mosić, Dijana
  • Kyrchei, Ivan I.

Abstract

New properties and representations for the core-EP inverse are developed. Particularly, the core-EP inverse of an upper triangular matrix and its sign pattern are considered. Determinantal representations for the core-EP inverse and core-EP solution of linear systems are investigated. Corresponding representations of the weighted core-EP inverse are derived. The obtained results are illustrated by computational algorithms and illustrative examples. Certain results related to the perturbation constraints for the core-EP inverse are also provided. The results related with the core-EP inverse are a continuous of the results from [H. Ma and P.S. Stanimirović, Characterizations, approximation and perturbations of the Core-EP inverse, Appl. Math. Comput. 359 (2019), 404–417].

Suggested Citation

  • Ma, Haifeng & Stanimirović, Predrag S. & Mosić, Dijana & Kyrchei, Ivan I., 2021. "Sign pattern, usability, representations and perturbation for the core-EP and weighted core-EP inverse," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321003374
    DOI: 10.1016/j.amc.2021.126247
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    References listed on IDEAS

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    1. Ivan I. Kyrchei, 2019. "Determinantal Representations of the Core Inverse and Its Generalizations with Applications," Journal of Mathematics, Hindawi, vol. 2019, pages 1-13, October.
    2. Kyrchei, Ivan, 2015. "Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 453-465.
    3. Ivan I. Kyrchei, 2016. "Explicit Determinantal Representation Formulas of -Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-13, June.
    4. Ma, Haifeng & Stanimirović, Predrag S., 2019. "Characterizations, approximation and perturbations of the core-EP inverse," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 404-417.
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    Cited by:

    1. Jin Zhong & Lin Lin, 2023. "Core-EP Monotonicity Characterizations for Property- n Matrices," Mathematics, MDPI, vol. 11(11), pages 1-11, May.

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