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Normal forms of regular matrix polynomials via local rank factorization

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  • Massimo Franchi

    ()
    ("Sapienza" Universita' di Roma)

  • Paolo Paruolo

    ()
    (Universita dell'Insubria)

Abstract

The `local rank factorization' (lrf) of a regular matrix polynomial at an eigenvalue consists of a sequence of matrix rank factorizations of a certain function of its coecients; the lrf delivers the local Smith form and extended canonical systems of root functions that correspond to the eigenvalue. In this paper it is shown that by performing the lrf at each finite eigenvalue and at infinity one can contruct the Smith form, Jordan triples and decomposable pairs of the matrix polynomial. When A(l) = A-lB, where A,B belong to C(pxp), the analysis delivers the Kronecker form of A(l) and strict similarity transformations; for B = I one finds the Jordan form of A and Jordan bases.

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File URL: http://www.dss.uniroma1.it/RePec/sas/wpaper/20111_Franchi_Paruolo.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome in its series DSS Empirical Economics and Econometrics Working Papers Series with number 2011/1.

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Length: 15 pages
Date of creation: Jul 2011
Date of revision:
Handle: RePEc:sas:wpaper:20111

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Related research

Keywords: Poolability; Matrix polynomials; spectral theory; canonical forms; Smith form; Kronecker form; Jordan form; Jordan chains; Jordan pairs; Jordan triples;

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  1. Johansen, Søren, 1992. "A Representation of Vector Autoregressive Processes Integrated of Order 2," Econometric Theory, Cambridge University Press, vol. 8(02), pages 188-202, June.
  2. Franchi, Massimo, 2010. "A Representation Theory For Polynomial Cofractionality In Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1201-1217, August.
  3. Haldrup, Niels & Salmon, Mark, 1998. "Representations of I(2) cointegrated systems using the Smith-McMillan form," Journal of Econometrics, Elsevier, vol. 84(2), pages 303-325, June.
  4. Franchi, Massimo & Paruolo, Paolo, 2011. "A characterization of vector autoregressive processes with common cyclical features," Journal of Econometrics, Elsevier, vol. 163(1), pages 105-117, July.
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