A note on similarity to contraction for stable $2 \times 2$ companion matrices
We consider companion matrices of size $2 \times 2$ with general complex spectra satisfying a root condition with respect to the closed complex unit circle or the closed left complex half plane. For both cases, smooth and naturally conditioned basis transformations are constructed such that the resu...
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| Date: | 2016 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2016
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1847 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We consider companion matrices of size $2 \times 2$ with general complex spectra satisfying a root condition with respect to the closed complex unit circle or the closed left complex half plane. For both cases, smooth and naturally conditioned basis transformations are constructed such that the resulting, transformed matrix is contractive or dissipative, respectively, with
respect to the $\ell_2$-norm. |
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