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    On the conjugate product of complex polynomial matrices

    Access Status
    Open access via publisher
    Authors
    Wu, A.
    Liu, Wan-Quan
    Duan, G.
    Date
    2011
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Wu, A. and Liu, W. and Duan, G. 2011. On the conjugate product of complex polynomial matrices. Mathematical and Computer Modelling. 53 (9-10): pp. 2031-2043.
    Source Title
    Mathematical and Computer Modelling
    DOI
    10.1016/j.mcm.2010.12.027
    ISSN
    0895-7177
    School
    Department of Computing
    URI
    http://hdl.handle.net/20.500.11937/36661
    Collection
    • Curtin Research Publications
    Abstract

    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).

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