Locally Invertible Multivariate Polynomial Matrices

  • Ruben G. Lobo
  • Donald L. Bitzer
  • Mladen A. Vouk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)


A new class of rectangular zero prime multivariate polynomial matrices are introduced and their inverses are computed. These matrices are ideal for use in multidimensional systems involving input-output transformations. We show that certain multivariate polynomial matrices, when transformed to the sequence space domain, have an invertible subsequence map between their input and output sequences. This invertible subsequence map can be used to derive the polynomial inverse matrix together with a set of pseudo-inverses. All computations are performed using elementary operations on the ground field without using any polynomial operations.


Sequence Space Input Sequence Polynomial Matrix Output Sequence Input Symbol 
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  1. 1.
    Bose, N.K. (ed.): Multidimensional Systems: Progress, Directions and Open Problems. Reidel, Dordrecht, The Netherlands (1985)Google Scholar
  2. 2.
    Youla, D.C., Gnavi, G.: Notes on n-dimensional system theory. IEEE Trans. Circuits and Systems 26, 105–111 (1979)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Youla, D., Pickel, P.: The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices. IEEE Trans. Circuits and Systems 31(6), 513–517 (1984)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Park, H., Kalker, T., Vetterli, M.: Grobner bases and multidimensional FIR multirate systems. Journal of multidimensional systems and signal processing 8, 11–30 (1997)CrossRefMATHGoogle Scholar
  5. 5.
    Fornasini, E., Valcher, M.E.: nD polynomial matrices with applications to multidimensional signal analysis. Multidimensional Systems and Signal Processing 8, 387–408 (1997)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Fornasini, E., Valcher, M.E.: Algebraic aspects of 2D convolutional codes. IEEE Trans. Inform. Theory IT-40(4), 1068–1082 (1994)CrossRefMATHGoogle Scholar
  7. 7.
    Weiner, P.A.: Basic properties of multidimensional convolutional codes. In: Codes, Systems and Graphical Models. IMA Volumes in Mathematics and Its Applications, vol. 123, pp. 397–414. Springer, New York (2001)CrossRefGoogle Scholar
  8. 8.
    Luerssen, H.G., Rosenthal, J., Weiner, P.A.: Duality between multidimensional convolutional codes and systems. In: Colonius, F., Helmke, U., Wirth, F., Prätzel-Wolters, D. (eds.) Advances in Mathematical Systems Theory, A Volume in Honor of Diederich Hinrichsen, Birkhauser, Boston, pp. 135–150 (2000)Google Scholar
  9. 9.
    Vologiannidis, S., Karampetakis, N.: Inverses of multivariable polynomial matrices by discrete fourier transforms. Multidimensional Systems and Signal Processing 15(4), 341–361 (2004)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Lobo, R.G., Bitzer, D.L., Vouk, M.A.: Locally invertible multivariate polynomial matrices. In: Ytrehus, Ø. (ed.) WCC 2005. LNCS, vol. 3969, pp. 481–490. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ruben G. Lobo
    • 1
  • Donald L. Bitzer
    • 1
  • Mladen A. Vouk
    • 1
  1. 1.North Carolina State UniversityRaleighUSA

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