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Factorizations for a class of multivariate polynomial matrices

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Abstract

This paper investigates how to factorize a class of multivariate polynomial matrices. We prove that an \(l\times m\) multivariate polynomial matrix admits a matrix factorization with respect to a given polynomial if the polynomial and all the \((l-1)\times (l-1)\) reduced minors of the matrix generate a unit ideal. This result is a generalization of a theorem in Liu et al. (Circuits Syst Signal Process 30(3):553–566, 2011). Based on three main theorems presented in the paper and a constructive algorithm proposed by Lin et al. (Circuits Syst Signal Process 20(6):601–618, 2001), we give an algorithm which can be used to factorize more multivariate polynomial matrices. In addition, an illustrative example is given to show the effectiveness of the proposed algorithm.

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Authors and Affiliations

  1. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China

    Dong Lu

  2. School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Dong Lu

  3. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Dingkang Wang & Fanghui Xiao

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Dingkang Wang & Fanghui Xiao

Authors
  1. Dong Lu
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  2. Dingkang Wang
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  3. Fanghui Xiao
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Correspondence to Dingkang Wang.

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This research was supported by the Chinese Academy of Sciences Key Project QYZDJ-SSW-SYS022.

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Lu, D., Wang, D. & Xiao, F. Factorizations for a class of multivariate polynomial matrices. Multidim Syst Sign Process 31, 989–1004 (2020). https://doi.org/10.1007/s11045-019-00694-z

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  • DOI: https://doi.org/10.1007/s11045-019-00694-z

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