Acta mathematica scientia,Series B ›› 2005, Vol. 25 ›› Issue (1): 112-118.

• Articles • Previous Articles     Next Articles

REMARKS ON BRUALDI’S THEOREM FOR SPECTRUM INCLUSION REGION OF AN IRREDUCIBLE MATRIX

 CHEN Shen-Can   

  • Online:2005-01-20 Published:2005-01-20
  • Supported by:

    This work is supported by the Natural Science Foundation of Fujian Education
    Committee (JA04157)

Abstract:

This paper obtains a necessary and sufficient condition for an irreducible com-
plex matrix whose comparison matrix is a singular M-matrix to be singular. This is used
to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion
region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.

Key words: M-matrix;irreducible circuit -diagonal dominant matrix;spectrum inclu-
sion region

CLC Number: 

  • 15A57
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