Abstract
Definitions of certain spectral characteristics of polynomial matrices (such as the analytical (algebraic) and geometric multiplicities of a point of the spectrum, deflating subspaces, matrix solvents, and block eigenvalues and eigenvectors) are generalized to the multiparameter case, and properties of these characteristics are analyzed. Bibliogrhaphy: 4 titles.
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REFERENCES
V. B. Khazanov, “On some spectral characteristics of λ-matrices,” Zap. Nauchn. Semin. POMI, 139, 111–124 (1984).
V. B. Khazanov, “On spectral properties of multiparameter polynomial matrices,” Zap. Nauchn. Semin. POMI, 229, 284–321 (1995).
V. B. Khazanov, “Generating eigenvectors of a multiparameter polynomial matrix,” Zap. Nauchn. Semin. POMI, 248, 165–186 (1998).
V. B. Khazanov, “On some properties of polynomial bases of subspaces over the field of rational functions in several variables,” Zap. Nauchn. Semin. POMI, 284, 177–191 (2002).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 166–173.
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Khazanov, V.B. On Some Spectral Characteristics of Multiparameter Polynomial Matrices. J Math Sci 132, 236–239 (2006). https://doi.org/10.1007/s10958-005-0492-5
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DOI: https://doi.org/10.1007/s10958-005-0492-5