The Drazin inverses of Combinations of Two idempotents

Authors

  • Tao Xie Hubei Normal University
  • Kezheng Zuo Hubei Normal University

Keywords:

Idempotent operator, Drazin inverse, combination

Abstract

By using the methods of splitting operator's matrix into blocks and space decompositions, the existence and calculation formulas of Drazin inverse of the combinations aP+bQ+cPQ of two idempotent operators P and Q on a Hilbert space are obtained under the conditions PQP=0,PQP=P and PQP=PQ respectively.These generalized the related results of Deng's work, which characterized the Drazin inverse of the sum and difference of two idempotents.

Author Biographies

  • Tao Xie, Hubei Normal University
    Math department
  • Kezheng Zuo, Hubei Normal University

    Math Department

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Published

2012-11-07

Issue

Vol. 5 No. 4: (October 2012)

Section

Mathematical Modeling and Numerical Analysis

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How to Cite

The Drazin inverses of Combinations of Two idempotents. (2012). European Journal of Pure and Applied Mathematics, 5(4), 480-491. https://www.ejpam.com/index.php/ejpam/article/view/1624