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Eigenvalue problem for an irregular λ-matrix

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Abstract

The solution of the eigenvalue problem is examined for the polyńomial matrixD(λ)=Aoλs+A1λs−1+...+As when the matricesA 0 andA 2 (or one of them) are singular. A normalized process is used for solving the problem, permitting the determination of linearly independent eigenvectors corresponding to the zero eigenvalue of matrixD(λ) and to the zero eigenvalue of matrixA 0. The computation of the other eigenvalues ofD(λ) is reduced to the same problem for a constant matrix of lower dimension. An ALGOL program and test examples are presented.

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Literature cited

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Authors
  1. V. N. Kublanovskaya
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  2. V. B. Mikhailov
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  3. V. B. Khazanov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 58, pp. 80–92, 1976.

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Kublanovskaya, V.N., Mikhailov, V.B. & Khazanov, V.B. Eigenvalue problem for an irregular λ-matrix. J Math Sci 13, 251–260 (1980). https://doi.org/10.1007/BF01296241

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  • DOI: https://doi.org/10.1007/BF01296241

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