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Journal of Mathematical Sciences

, Volume 165, Issue 5, pp 574–588 | Cite as

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

  • V. N. Kublanovskaya
Article
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This paper continues the series of publications devoted to surveying and developing methods for solving the following problems for a two-parameter matrix F (λ, μ) of general form: exhausting points of the mixed regular spectrum of F (λ, μ); performing operations on polynomials in two variables (computing the GCD and LCM of a few polynomials, division of polynomials, and factorization); computing a minimal basis of the null-space of polynomial solutions of the matrix F (λ, μ) and separation of its regular kernel; inversion and pseudo in version of polynomial and rational matrices in two variables, and solution of systems of nonlinear algebraic equations in two unknowns. Most of the methods suggested are based on rank factorizations of a two-parameter polynomial matrix and on the method of hereditary pencils. Bibliography: 8 titles.

Keywords

Russia Algebraic Equation Mathematical Institute Rational Matrice Polynomial Matrix 
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References

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    V. N. Kublanovskaya, “To solving problems of algebra for two-parameter matrices. 1,” Zap. Nauchn. Semin. POMI, 359, 107–149 (2008).Google Scholar
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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