Skip to main content
SpringerLink
Log in

Notes on factor prime factorizations for n-D polynomial matrices

  • Communication Brief
  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

Multidimensional (n−D) polynomial matrix factorizations have been widely investigated during the past years due to the fundamental importance in the areas of multidimensional systems and signal processing. This note is a continuation of the papers in Wang (Circuits Syst I 54: 1398–1405, 2007 and Circuits Syst II 55: 61–64, 2008). A complete constructive criterion is given for a matrix of 2 × m full row rank to be FLP. We also present a reduction method for dealing with the factorization problems with cases of non-regular divisors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Bose N.K. (1982) Applied multidimensional systems theory. Van Nostrand Reinhold, New York

    MATH  Google Scholar 

  • Bose N.K., Buchberger B., Guiver J.P. (2003) Multidimensional systems theory and applications. Kluwer, Dordrecht, The Netherlands

    MATH  Google Scholar 

  • Charoenlarpnopparut C., Bose N.K. (1999) Multidimensional FIR filter bank design using Gröbner bases. IEEE Transactions On Circuits and Systems-II: Analog and Digital Signal Processing 46(12): 1475–1486

    Article  MATH  Google Scholar 

  • Fornasini E., Valcher M.E. (1997) n-D polynomial matrices with applications to multidimensional signal analysis. Multidimensional Systems and Signal Processing 8: 387–408

    Article  MATH  MathSciNet  Google Scholar 

  • Greuel G.M., Pfister G. (2008) A singular introduction to commutative algebra (2nd ed). Springer, Heidelberg

    Google Scholar 

  • Guiver J.P., Bose N.K. (1982) Polynomial matrix factorization over arbitrary coefficient field and related results. IEEE Transactions on Circuits and Systems, CAS- 29(10): 649–657

    Article  MATH  MathSciNet  Google Scholar 

  • Lam T.Y. (2006) Serre’s problem on projective module. Springer-Verlag, Berlin, Germany

    Google Scholar 

  • Lin Z. (1988) On matrix fraction description of multivariable linear n-D systems. IEEE Transactions on Circuits and Systems 35(10): 1317–1322

    Article  MATH  Google Scholar 

  • Lin Z. (1992) On primitive factorizations for 3-D polynomial matrices. IEEE Transactions on Circuits and Systems 39(12): 1024–1027

    Article  MATH  MathSciNet  Google Scholar 

  • Lin Z. (1999) Notes on n-D polynomial matrix factorization. Multidimensional Systems and Signal Processing 10: 379–393

    Article  MATH  MathSciNet  Google Scholar 

  • Lin Z., Bose N.K. (2001) A generalization of Serre’s conjecture and related issues. Linear Algebra and Its Applications 338: 125–138

    Article  MATH  MathSciNet  Google Scholar 

  • Lin Z., Xu L., Bose N.K. (2008) A tutorial on Gröbner bases with applications in signals and systems. IEEE Transactions on Circuits Systems I 55(1): 445–461

    Article  MathSciNet  Google Scholar 

  • Lin Z., Xu L., Fan H. (2005) On minor prime factorization for n-D polynomial matrices. IEEE Transactions on Circuits and Systems II: Express Briefs 52(9): 568–571

    Article  Google Scholar 

  • Lin Z., Ying J.Q., Xu L. (2001) Factorizations for nD polynomial matrices. Circuits, Systems, and Signal Processing 20: 601–618

    Article  MATH  MathSciNet  Google Scholar 

  • Morf M., Levy B.C., Kung S.Y. (1977) New results in 2-D systems theory, part I: 2-D polynomial matrices, factorizations and coprimeness. Proceedings of the IEEE 65(4): 861–872

    Article  Google Scholar 

  • Pommaret, J. F. (2001). Solving Bose conjecture on linear multidimensional systems. In: Proceedings of the European Control Conference (pp. 1853–1855).

  • Srinivas V. (2004) A generalized Serre problem. Journal of Algebra 278(2): 621–627

    Article  MATH  MathSciNet  Google Scholar 

  • Wang M. (2007) On factor prime factorization for n-D polynomial matrices. IEEE Transactions on Circuits and Systems I: Regular Papers 54(6): 1398–1405

    Article  MathSciNet  Google Scholar 

  • Wang M. (2008) Remarks on n-D polynomial matrix factorization problems. IEEE Transactions on Circuits and Systems II: Express Briefs 55(1): 61–64

    Article  Google Scholar 

  • Wang M., Feng D. (2004) On Lin–Bose problem. Linear Algebra and its Applications 390: 279–285

    Article  MATH  MathSciNet  Google Scholar 

  • Wang M., Kwong C.P. (2005) On multivariate polynomial matrix factorization problems. Mathematics of Control, Signals, and Systems 17(4): 297–311

    Article  MATH  MathSciNet  Google Scholar 

  • Wood J., Rogers E., Owens H. (1998) A formal theory of matrix primeness. Mathematics of Control, Signals, and Systems 11: 40–78

    Article  MATH  MathSciNet  Google Scholar 

  • Youla D.C., Gnavi G. (1979) Notes on n-dimensional system theory. IEEE Transactions on Circuits and Systems CAS- 26(2): 105–111

    Article  MATH  MathSciNet  Google Scholar 

  • Youla D.C., Pickel P.F. (1984) The Quillen–Suslin theorem and the structure of n-dimensional elementary polynomial matrices. IEEE Transactions on Circuits and Systems CAS- 31(6): 513–518

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Computational Science, Hunan University of Sciences and Technology, Xiangtan, People’s Republic of China

    Jinwang Liu

  2. State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, 100190, Beijing, China

    Mingsheng Wang

Authors
  1. Jinwang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mingsheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mingsheng Wang.

Additional information

This work was supported in part by the National Science Foundation of China under Grant 10771058, and by 973 project under Grant (2007CB311201).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, J., Wang, M. Notes on factor prime factorizations for n-D polynomial matrices. Multidim Syst Sign Process 21, 87–97 (2010). https://doi.org/10.1007/s11045-009-0089-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-009-0089-0

Keywords

Search

Navigation