On the conjugate product of complex polynomial matrices
In this paper, we propose a new operator of conjugate product for complex polynomial matrices. Elementary transformations are first investigated for the conjugate product. It is shown that an arbitrary complex polynomial matrix can be converted into the so-called Smith normal form by elementary tran...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/36661 |
| _version_ | 1848754832570056704 |
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| author | Wu, A. Liu, Wan-Quan Duan, G. |
| author_facet | Wu, A. Liu, Wan-Quan Duan, G. |
| author_sort | Wu, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we propose a new operator of conjugate product for complex polynomial matrices. Elementary transformations are first investigated for the conjugate product. It is shown that an arbitrary complex polynomial matrix can be converted into the so-called Smith normal form by elementary transformations in the framework of conjugate product. Then the concepts of greatest common divisors and coprimeness are proposed and investigated, and some necessary and sufficient conditions for the coprimeness are established. Finally, it is revealed that two complex matrices A and B are consimilar if and only if (sI−A) and (sI−B) are conequivalent. Such a fact implies that the Jordan form of a complex matrix AA under consimilarity may be obtained by analyzing the Smith normal form of (sI−A). |
| first_indexed | 2025-11-14T08:46:41Z |
| format | Journal Article |
| id | curtin-20.500.11937-36661 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:46:41Z |
| publishDate | 2011 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-366612017-09-13T15:29:12Z On the conjugate product of complex polynomial matrices Wu, A. Liu, Wan-Quan Duan, G. In this paper, we propose a new operator of conjugate product for complex polynomial matrices. Elementary transformations are first investigated for the conjugate product. It is shown that an arbitrary complex polynomial matrix can be converted into the so-called Smith normal form by elementary transformations in the framework of conjugate product. Then the concepts of greatest common divisors and coprimeness are proposed and investigated, and some necessary and sufficient conditions for the coprimeness are established. Finally, it is revealed that two complex matrices A and B are consimilar if and only if (sI−A) and (sI−B) are conequivalent. Such a fact implies that the Jordan form of a complex matrix AA under consimilarity may be obtained by analyzing the Smith normal form of (sI−A). 2011 Journal Article http://hdl.handle.net/20.500.11937/36661 10.1016/j.mcm.2010.12.027 unknown |
| spellingShingle | Wu, A. Liu, Wan-Quan Duan, G. On the conjugate product of complex polynomial matrices |
| title | On the conjugate product of complex polynomial matrices |
| title_full | On the conjugate product of complex polynomial matrices |
| title_fullStr | On the conjugate product of complex polynomial matrices |
| title_full_unstemmed | On the conjugate product of complex polynomial matrices |
| title_short | On the conjugate product of complex polynomial matrices |
| title_sort | on the conjugate product of complex polynomial matrices |
| url | http://hdl.handle.net/20.500.11937/36661 |