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Journal of Mathematical Sciences

, Volume 176, Issue 1, pp 78–82 | Cite as

To solving problems of algebra for two-parameter matrices. VII

  • V. N. Kublanovskaya
  • V. B. Khazanov
Article
  • 23 Downloads

The paper discusses the method of rank factorization for solving spectral problems for two-parameter polynomial matrices. New forms of rank factorization, which are computed using unimodular matrices only, are suggested. Applications of these factorizations to solving spectral problems for two-parameter polynomial matrices of both general and special forms are presented. In particular, matrices free of the singular spectrum are considered. Conditions sufficient for a matrix to be free of the singular spectrum and also conditions sufficient for a basis matrix of the null-space to have neither the finite regular nor the finite singular spectrum are provided. Bibliography: 3 titles.

Keywords

Russia Special Form Spectral Problem Mathematical Institute Basis Matrix 
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References

  1. 1.
    V. N. Kublanovskaya, “To solving problems of algebra for two-parameter matries. 1,” Zap. Nauhn. Semin, POMI, 359, 107–149 (2008).MathSciNetGoogle Scholar
  2. 2.
    V. N. Kublanovskaya and V. B. Khazanov, Numerial Methods for Solwing Parametric Problems of Algebra. Part1. One-Parameter Problems [inRussian], Nauka, St. Petersburg (2004).Google Scholar
  3. 3.
    V. B. Khazanov, “On some properties of polynomial bases of subspaces over the field of rational funtions in several variables,” Zap. Nauhn. Semin. POMI, 284, 177–191 (2002).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg State Marine Technical UniversitySt. PetersburgRussia

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