| A New Class of Minimally Spectrally Arbitrary Sign Patterns |
| Received:May 10, 2007 Revised:January 02, 2008 |
| Key Words:
sign pattern potentially nilpotent spectrally arbitrary pattern.
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| Fund Project:the National Natural Science Foundation of China (No.10571163); the Natural Science Foundation of Shanxi Province (No.20041010; 2007011017). |
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| Abstract: |
| If every monic real polynomial of degree $n$ can be achieved as the characteristic polynomial of some matrix $B\in Q(A)$, then sign pattern $A$ of order $n$ is a spectrally arbitrary pattern. A sign pattern $A$ is minimally spectrally arbitrary if it is spectrally arbitrary but is not spectrally arbitrary if any nonzero entry (or entries) of $A$ is replaced by zero. In this article, we give some new sign patterns which are minimally spectrally arbitrary for order $n\geq 9$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.02.020 |
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