Abstract
For a q-parameter polynomial m × n matrix F of rank ρ, solutions of the equation Fx = 0 at points of the spectrum of the matrix F determined by the (q −1)-dimensional solutions of the system Z[F] = 0 are considered. Here, Z[F] is the polynomial vector whose components are all possible minors of order ρ of the matrix F. A classification of spectral pairs in terms of the matrix A[F], with which the vector Z[F] is associated, is suggested. For matrices F of full rank, a classification and properties of spectral pairs in terms of the so-called levels of heredity of points of the spectrum of F are also presented. Bibliography: 4 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 132–149.
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Kublanovskaya, V.N. To solving multiparameter problems of algebra. 6. Spectral characteristics of polynomial matrices. J Math Sci 137, 4835–4843 (2006). https://doi.org/10.1007/s10958-006-0281-9
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DOI: https://doi.org/10.1007/s10958-006-0281-9