Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A SPECTRALLY ARBITRARY COMPLEX SIGN PATTERN

  • Liu, Sujuan (Department of Mathematics, North University of China) ;
  • Lei, Yingjie (Department of Mathematics, North University of China) ;
  • Gao, Yubin (Department of Mathematics, North University of China)
  • Published : 2010.01.30
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Abstract

A spectrally arbitrary complex sign pattern A is a complex sign pattern of order n such that for every monic nth degree polynomial f(x) with coefficients from $\mathbb{C}$, there is a matrix in the qualitative class of A having the characteristic polynomial f(x). In this paper, we show a necessary condition for a spectrally arbitrary complex sign pattern and introduce a minimal spectrally arbitrary complex sign pattern $A_n$ all of whose superpatterns are also spectrally arbitrary for $n\;{\geq}\;2$. Furthermore, we study the minimum number of nonzero parts in a spectrally arbitrary complex sign pattern.

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References

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