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

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The paper continues the series of papers devoted to surveying and developing methods for solving algebraic problems for two-parameter polynomial and rational matrices of general form. It considers linearization methods, which allow one to reduce the problem of solving an equation F(λ, µ)x = 0 with a polynomial two-parameter matrix F(λ, µ) to solving an equation of the form D(λ, µ)y = 0, where D(λ, µ) = A(µ)-λB(µ) is a pencil of polynomial matrices. Consistent pencils and their application to solving spectral problems for the matrix F(λ, µ) are discussed. The notion of reducing subspace is generalized to the case of a pencil of polynomial matrices. An algorithm for transforming a general pencil of polynomial matrices to a quasitriangular pencil is suggested. For a pencil with multiple eigenvalues, algorithms for computing the Jordan chains of vectors are developed. Bibliography: 8 titles.

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References

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Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    V. N. Kublanovskaya

  2. St.Petersburg State Marine Technical University, St.Petersburg, Russia

    V. B. Khazanov

Authors
  1. V. N. Kublanovskaya
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  2. V. B. Khazanov
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Correspondence to V. N. Kublanovskaya.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 359, 2008, pp. 166–207.

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Kublanovskaya, V.N., Khazanov, V.B. To solving problems of algebra for two-parameter matrices. III. J Math Sci 157, 761–783 (2009). https://doi.org/10.1007/s10958-009-9359-5

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  • DOI: https://doi.org/10.1007/s10958-009-9359-5

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