| The Nilpotent-Centralizer Methods |
| Received:October 28, 2013 Revised:June 18, 2014 |
| Key Words:
complex sign pattern ray pattern spectrally arbitrary pattern nilpotence.
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| Fund Project:Supported by National Natural Science Foundation of China (Grant No.11071227) and Shanxi Scholarship Council of China (Grant No.12-070). |
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| Abstract: |
| An $n \times n$ complex sign pattern (ray pattern) ${\cal S}$ is said to be spectrally arbitrary if for every monic $n$th degree polynomial $f(\lambda)$ with coefficients from $\mathbb{C}$, there is a complex matrix in the complex sign pattern class (ray pattern class) of ${\cal S}$ such that its characteristic polynomial is $f(\lambda)$. We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns, respectively. We find that the Nilpotent-Centralizer methods for three kinds of patterns (sign pattern, complex sign pattern, ray pattern) are the same in form. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.05.010 |
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