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Czechoslovak Mathematical Journal

, Volume 64, Issue 4, pp 883–892 | Cite as

On block triangular matrices with signed Drazin inverse

  • Changjiang Bu
  • Wenzhe Wang
  • Jiang Zhou
  • Lizhu Sun
Article

Abstract

The sign pattern of a real matrix A, denoted by sgnA, is the (+, −, 0)-matrix obtained from A by replacing each entry by its sign. Let Q(A) denote the set of all real matrices B such that sgnB = sgnA. For a square real matrix A, the Drazin inverse of A is the unique real matrix X such that A k+1 X = A k , XAX = X and AX = XA, where k is the Drazin index of A. We say that A has signed Drazin inverse if \(\operatorname{sgn} {\tilde A^d} = \operatorname{sgn} {A^d}\) for any \(\tilde A \in Q(A)\), where A d denotes the Drazin inverse of A. In this paper, we give necessary conditions for some block triangular matrices to have signed Drazin inverse.

Keywords

sign pattern matrix signed Drazin inverse strong sign nonsingular matrix 

MSC 2010

15B35 15A09 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  • Changjiang Bu
    • 1
  • Wenzhe Wang
    • 1
  • Jiang Zhou
    • 2
  • Lizhu Sun
    • 3
  1. 1.College of ScienceHarbin Engineering UniversityHarbinHeilongjiang Province, P.R. China
  2. 2.College of Computer Science and Technology, and College of ScienceHarbin Engineering UniversityHarbinHeilongjiang Province, P.R. China
  3. 3.School of ScienceHarbin Institute of TechnologyHarbinHeilongjiang Province, P.R. China

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