×

Inertia characteristics of self-adjoint matrix polynomials. (English) Zbl 0516.15018


MSC:

15A54 Matrices over function rings in one or more variables
15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anderson, B. D.O.; Jury, E. I., Generalized Bezoutian and Sylvester matrices in multivariable linear control, IEEE Trans. Automat. Control, AC-21, 551-556 (1976) · Zbl 0332.93032
[2] Barnett, S.; Lancaster, P., Some properties of the Bezoutian for polynomial matrices, Linear and Multilinear Algebra, 9, 99-110 (1980) · Zbl 0504.15002
[3] Carlson, D.; Schneider, H., Inertia theorems for matrices: the semidefinite case, J. Math. Anal. Appl., 6, 430-446 (1963) · Zbl 0192.13402
[4] Daleckii, J. L.; Krein, M. G., Stability of Solutions of Differential Equations in Banach Spaces, Amer. Math. Soc. Translations, Vol. 43 (1974), Providence · Zbl 0286.34094
[5] Datta, B. N., On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem, Linear Algebra Appl, 22, 235-246 (1978) · Zbl 0387.15011
[6] Datta, B. N., An elementary proof of the stability criterion of Liénard and Chipart, Linear Algebra Appl., 22, 89-96 (1978) · Zbl 0402.15005
[7] Gantmacher, F. R., The Theory of Matrices, Vols. I, II (1959), Chelsea, New York · Zbl 0085.01001
[8] Gohberg, I.; Kaashoek, M. A.; Lerer, L.; Rodman, L., Common multiples and common divisors of matrix polynomials, I Spectral method, Indiana Univ. Math. J., 30, 321-356 (1981) · Zbl 0449.15015
[9] Gohberg, I.; Lancaster, P.; Rodman, L., Spectral analysis of selfadjoint matrix polynomials, Ann. of Math., 112, 34-71 (1980) · Zbl 0446.15007
[10] Gohberg, I.; Lancaster, P.; Rodman, L., Matrix Polynomials (1982), Academic: Academic New York · Zbl 0482.15001
[11] Krein, M. G.; Naimark, M. A., The method of symmetric and hermitian forms in the theory of the separation of the roots of algebraic equations, Linear and Multilinear Algebra, 10, 265-308 (1981) · Zbl 0584.12018
[12] Lancaster, P., Lambda Matrices and Vibrating Systems (1966), Pergamon: Pergamon Oxford · Zbl 0146.32003
[13] Lancaster, P., Symmetric transformation of the companion matrix, NABLA, Bull. Malayan Math. Soc., 8, 146-148 (1961)
[14] P. Lancaster and M. Tismenetsky, Some extensions and modifications of classical stability tests for polynomials, Inter. J. Control; P. Lancaster and M. Tismenetsky, Some extensions and modifications of classical stability tests for polynomials, Inter. J. Control · Zbl 0526.93043
[15] Lerer, L.; Tismenetsky, M., The Bezoutian and the eigenvalue-separation problem for matrix polynomials, Integral Eq. Operator Theory, 5, 386-445 (1982) · Zbl 0504.47020
[16] L. Lerer and M. Tismenetsky, Quasilinearizations of Matrix Polynomials (in preparation).; L. Lerer and M. Tismenetsky, Quasilinearizations of Matrix Polynomials (in preparation). · Zbl 0587.15008
[17] Ostrowsky, A.; Schneider, H., Some theorems on the inertia of general matrices, J. Math. Anal. Appl., 4, 72-84 (1962) · Zbl 0112.01401
[18] Taussky, O., A generalization of a theorem by Lyapunov, J. Soc. Ind. Appl. Math., 9, 640-643 (1961) · Zbl 0108.01202
[19] Wimmer, H. K., Inertia theorems for matrices, controllability and linear vibrations, Lin. Alg. Appl., 8, 337-343 (1974) · Zbl 0288.15015
[20] Yakubovich, V. A.; Starzhinskii, V. M., Linear Differential Equations with Periodic Coefficients (1975), Wiley: Wiley New York · Zbl 0308.34001
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.