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To solving multiparameter problems of algebra. 6: Spectral characteristics of polynomial matrices. (Russian, English) Zbl 1117.65320

Zap. Nauchn. Semin. POMI 323, 132-149 (2005); translation in J. Math. Sci., New York 137, No. 3, 4835-4843 (2007).
Summary: For a \(q\)-parameter polynomial \(m\times n\) matrix \(F\) of rank \(\rho\), 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 \(\rho\) 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.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A54 Matrices over function rings in one or more variables
15A18 Eigenvalues, singular values, and eigenvectors
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