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Construction of a canonic basis for matrices and pencils of matrices

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Abstract

An algorithm is offered, which with insignificant modifications permits; 1) the finding of a canonic basis of the root sub space corresponding to a prescribed eigenvalue of a matrix; 2) the finding of chains of associated vectors to the eigenvectors corresponding to a prescribed eigenvalue of a regular linear pencil; 3) the finding of chains of generalized associated vectors corresponding to a prescribed eigenvalue of a regular kernel of a singular linear pencil of complete column rank of two matrices; 4) the finding of linearly independent polynomial solutions of a singular linear pencil. The algorithm consists in the construction of a finite sequence of certain auxiliary matrices the choice of which depends on the problem being solved and in the construction of a sequence of their null-spaces, enabling the obtaining of all necessary information on the unknown vectors of the canonic basis of the problem being solved.

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Literature cited

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Authors
  1. V. N. Kublanovskaya
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 90, pp. 46–62, 1979.

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Kublanovskaya, V.N. Construction of a canonic basis for matrices and pencils of matrices. J Math Sci 20, 1929–1942 (1982). https://doi.org/10.1007/BF01680564

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  • DOI: https://doi.org/10.1007/BF01680564

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