Previous |  Up |  Next


power and exponentially bounded matrices; spectral decomposition; Drazin inverse; singularly perturbed differential equations; asymptotic behaviour
The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.
[1] S. L. Campbell: Singular Systems of Differential Equations. Pitman, Boston, 1980. Zbl 0419.34007
[2] S. L. Campbell and C. D. Meyer: Generalized Inverses of Linear Transformations. Surveys and Reference Works in Mathematics, Pitman, London, 1979.
[3] A. S. Householder: Theory of Matrices in Numerical Analysis. Blaisdell, New York, 1964. MR 0175290 | Zbl 0161.12101
[4] Tai-Ping Liu: Resonance for quasilinear hyperbolic equation. Bull. Amer. Math. Soc. 6 (1982), 463–465. DOI 10.1090/S0273-0979-1982-15018-2 | MR 0648536
[5] I. Marek and K. Žitný: Matrix Analysis for Applied Sciences, volume 1, 2. Teubner-Texte zur Mathematik 60, 84, Teubner, Leipzig, 1983, 1986. MR 0731071
[6] B. Noble and J. W. Daniel: Applied Linear Algebra, 3rd edition. Prentice-Hall, Englewood Cliffs, 1988. MR 0572995
[7] U. G. Rothblum: A representation of the Drazin inverse and characterizations of the index. SIAM J. Appl. Math. 31 (1976), 646–648. DOI 10.1137/0131057 | MR 0422303 | Zbl 0355.15008
[8] U. G. Rothblum: Resolvent expansions of matrices and applications. Lin. Algebra Appl. 38 (1981), 33–49. DOI 10.1016/0024-3795(81)90006-9 | MR 0636023 | Zbl 0468.15002
[9] U. G. Rothblum: Expansions of sums of matrix powers. SIAM Review 23 (1981), 143–164. DOI 10.1137/1023036 | MR 0618637 | Zbl 0466.15005
Partner of
EuDML logo