Khazanov, V. B. On generating eigenvectors of multiparameter polynomial matrices. (English. Russian original) Zbl 0959.15007 J. Math. Sci., New York 101, No. 4, 3326-3337 (2000); translation from Zap. Nauchn. Semin. POMI 248, 165-186 (1998). Summary: The notion of a generating eigenvector of a multiparameter polynomial matrix, generalizing the notion of an eigenvector of a one-parameter polynomial matrix, is introduced. Some properties of generating eigenvectors are established, and two methods for constructing them are suggested. Cited in 2 Documents MSC: 15A18 Eigenvalues, singular values, and eigenvectors 15A54 Matrices over function rings in one or more variables Keywords:generating eigenvector; polynomial matrix × Cite Format Result Cite Review PDF Full Text: DOI References: [1] V. N. Kublanovskaya, ”An approach to solving multiparameter problems,”Zap. Nauchn. Semin. POMI,229, 191–246 (1995). · Zbl 0899.65022 [2] V. N. Kublanovskaya, ”Methods and algorithms for solving spectral problems for polynomial and rational matrices,”Zap. Nauchn. Semin. POMI,238, 3–330 (1997). · Zbl 0928.65064 [3] V. N. Kublanovskaya and V. N. Simonova, ”Operations on scalar polynomials and their computer implementation,”Zap. Nauchn. Semin. POMI,219, 158–176 (1994). · Zbl 0867.65005 [4] V. N. Kublanovskaya and V. B. Khazanov, ”Relative factorization of polynomials in several variables,”J. Vychisl. Mat. Mat. Fiz. 36, No. 8, 6–11 (1996). · Zbl 0911.65041 [5] V. B. Khazanov, ”On spectral properties of {\(\lambda\)}-matrices,”Zap. Nauchn. Semin. LOMI,111, 180–194 (1981). · Zbl 0496.15011 [6] V. B. Khazanov, ”On spectral properties of multiparameter polynomial matrices,”Zap. Nauchn. Semin. LOMI,229, 284–321 (1995). · Zbl 0899.15005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.