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Journal of Mathematical Sciences

, Volume 137, Issue 3, pp 4844–4851 | Cite as

To solving multiparameter problems of algebra. 7. The PG-q factorization method and its applications

  • V. N. Kublanovskaya
Article
  • 9 Downloads

Abstract

The paper continues the development of rank-factorization methods for solving certain algebraic problems for multi-parameter polynomial matrices and introduces a new rank factorization of a q-parameter polynomial m × n matrix F of full row rank (called the PG-q factorization) of the form F = PG, where \(P = \prod\limits_{k = 1}^{q - 1} {\prod\limits_{i = 1}^{n_k } {\nabla _i^{(k)} } } \) is the greatest left divisor of F; Δ i (k) i is a regular (q-k)-parameter polynomial matrix the characteristic polynomial of which is a primitive polynomial over the ring of polynomials in q-k-1 variables, and G is a q-parameter polynomial matrix of rank m. The PG-q algorithm is suggested, and its applications to solving some problems of algebra are presented. Bibliography: 6 titles.

Keywords

Characteristic Polynomial Polynomial Matrix Basis Matrix Irreducible Polynomial Factorization Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 5,” Zap. Nauchn. Semin. POMI, 309, 144–153 (2004).MATHGoogle Scholar
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    V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 2,” Zap. Nauchn. Semin. POMI, 296, 89–164 (2003).MATHGoogle Scholar
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    V. N. Kublanovskaya and V. B. Khazanov, “Relative factorization of polynomials in several variables, ” Zh. Vychisl. Matem. Matem. Fiz., 36, No. 8, 6–11 (1996).MATHMathSciNetGoogle Scholar
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    V. B. Khazanov, “On spectral properties of multiparameter polynomial matrices,” Zap. Nauchn. Semin. POMI, 229, 184–321 (1995).Google Scholar
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    V. N. Kublanovskaya, “An approach to solving multiparameter problems,” Zap. Nauchn. Semin. POMI, 229, 191–246 (1995).MATHGoogle Scholar
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    V. N. Kublanovskaya, “To solving multiparameter problems of algebra. 6,” Zap. Nauchn. Semin. POMI, 323, 132–149 (2005).MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. N. Kublanovskaya
    • 1
  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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