Abstract
The investigation of spectral properties and characteristics of λ-matrices of general form is continued. The concept of a matrix solution is extended to the case of singular λ-matrices. The concept of reducing subspaces and the concepts of a block eigenvalue and a block eigenvector are generalized. Existence theorems are proved; spectral properties of matrix quantities associated with the concepts indicated and their generalizations are established.
Similar content being viewed by others
Literature cited
L. M. Gryniv, “On separating out a special factor from a polynomial matrix,” Dokl. Akad. Nauk UkrSSR, A, No. 1, 11–13 (1981).
P. S. Kazimirskii and V. R. Zelisko, “On separating out a linear factor from a matrix polynomial,” Mat. Metody Fiz.-Mekh. Polya, No. 8, 10–16 (1978).
V. B. Khazanov, “On spectral properties of λ-matrices,” in: Numerical Methods and Questions of the Organization of Computations. 5. J. Sov. Math.,24, No. 1 (1984).
I. E. Dennis, I. F. Traub, and R. P. Weber, “On matrix polynomial, lambda-matrix, and block eigenvalue problems,” Cornell Univ., Carnegie-Mellon Univ., Computer Science Department Technical Report (1971).
P. Lancaster, λ-Matrices and Vibrating Systems, Pergamon Press (1966).
G. W. Stewart, “On the sensitivity of the eigenvalue problem Ax=λBx,” SIAM J. Numer. Anal.,9, No. 4, 669–686 (1972).
G. W. Stewart, “Error and perturbation bounds for subspaces associated with certain eigenvalue problems,” SIAM Rev.,15, No. 4, 727–764 (1973).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 139, pp. 111–124, 1984.
Rights and permissions
About this article
Cite this article
Khazanov, V.B. Some spectral characteristics of λ-matrices. J Math Sci 36, 251–261 (1987). https://doi.org/10.1007/BF01091805
Issue Date:
DOI: https://doi.org/10.1007/BF01091805