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Spectral analysis of regular matrix polynomials. (English) Zbl 0521.15015

MSC:
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15A54 Matrices over function rings in one or more variables
47A60 Functional calculus for linear operators
15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification
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[1] Bart, H., Gohberg, I. and Kaashoek, M.A.:Minimal factorizations of matrix and operator functions, Integral Equations & Operator Theory, Supplementary Series. · Zbl 0424.47001
[2] Bart, H., Gohbert, I. and Kaashoek, M.A.: A new characteristic operator function connected with operator polynomials, Wiskundig Seminarium der Vrije Universiteit, Amsterdam, Rapport No. 62, 1977.
[3] Bart, H., Gohberg, I. and Kaashoek, M.A.: Operator polynomials as inverses of characteristic functions,Integral Equations and Operator Theory 1 (1978), 1–12. · Zbl 0383.47012 · doi:10.1007/BF01682737
[4] Cohen, N.: On spectral analysis of matrix polynomials, M.Sc. Thesis, 1979, The Weizmann Institute of Science, Rehovot, Israel.
[5] Gantmacher, R.:The Theory of Matrices, Chelsea, N.Y. 1960 (Two volumes). · Zbl 0088.25103
[6] Gohberg, I., Kaashoek, M.A., Lerer, L. and Rodman, L.: Common multiples and common divisors of matrix polynomials, I. Spectral method,Indiana University Math. Journal 30.3 (1981), 321–356. · Zbl 0459.15015 · doi:10.1512/iumj.1981.30.30027
[7] Gohberg, I., Kaashoek, M.A. and Rodman, L. Spectral analysis of operator polynomials and a generalized Vandermonde matrix, I. The finite-dimensional case.Topics in Functional Analysis (Eds. I. Gohberg and M. Kac), Advances in Mathematics, Supplementary Studies, Vol. 3, New York, Academic Press (1978), 91–128. · Zbl 0453.15005
[8] Gohberg, I., Lancaster, P. and Rodman, L.: Spectral analysis of matrix polynomials, I. Canonical forms and divisors,Linear Algebra & Appl. 20 (1976), 1–44. · Zbl 0375.15008 · doi:10.1016/0024-3795(78)90026-5
[9] Gohberg, I., Lancaster, P. and Rodman, L.: Spectral analysis of matrix polynomials, II. The resolvent form and spectral divisors,Linear Algebra & Appl. 21 (1976), 65–88. · Zbl 0385.15007 · doi:10.1016/0024-3795(87)90201-1
[10] Gohberg, I., Lancaster, P. and Rodman, L.: Representations and divisibility of operator polynomials,Can. J. Math. 30 (1978), 1045–1069. · Zbl 0383.47020 · doi:10.4153/CJM-1978-088-2
[11] Gohberg, I. and Rodman, L.: On spectral analysis of non-monic matrix and operator polynomials. I. Reduction to monic polynomials,Israel J. Math. 30 (1978), 133–151. · Zbl 0396.47009 · doi:10.1007/BF02760835
[12] Gohberg, I. and Rodman, L.: On spectral analysis of non-monic matrix and operator polynomials. II. Dependence on the finite spectral data,Israel J. Math. 30 (1978), 321–334. · Zbl 0404.47012 · doi:10.1007/BF02761997
[13] Lancaster, P.:Theory of Matrices, Academic Press, N.Y., 1969. · Zbl 0186.05301
[14] Lancaster, P.: A fundamental theorem on \(\lambda\)-matrices, I–II,Linear Algebra & Appl. 18 (1977), 189–211 and 213–222. · Zbl 0388.15003 · doi:10.1016/0024-3795(77)90051-9
[15] Weierstrass, K.: Zur Theorie der bilinearen und quadratischen Formen,Monatsch. Akad. Wiss., Berlin, 1867. · JFM 01.0054.04
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