论文信息 - A Perturbation Bound for Definite Pencils

A Perturbation Bound for Definite Pencils

We attempt to generalize a well-known result on spectral variations of a Hermitian matrix due to Mirsky to the definite generalized eigenvalue problem. We also point out that some results on perturbations of definite pencils due to Stewart can be slightly improved.

Ren-Cang Li | Ren-Cang Li

[1] L. Mirsky. SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS , 1960 .

[2] Hideki Kosaki,et al. Inequalities for the Schatten p -norm V , 1987 .

[3] Y. Moon,et al. Finding a positive definite linear combination of two Hermitian matrices , 1983 .

[4] Ren-Cang Li. On perturbations of matrix pencils with real spectra , 1994 .

[5] Ji-guang Sun,et al. A note on Stewart's theorem for definite matrix pairs☆ , 1982 .

[6] R. Bhatia. Some inequalities for norm ideals , 1987 .

[7] H. Wielandt. An extremum property of sums of eigenvalues , 1955 .

[8] G. Stewart,et al. Matrix Perturbation Theory , 1990 .

[9] Ji-guang Sun. The perturbation bounds for eigenspaces of a definite matrix-pair , 1983 .

[10] William Kahan,et al. Some new bounds on perturbation of subspaces , 1969 .

[11] C. R. Crawford. A Stable Generalized Eigenvalue Problem , 1976 .

[12] R. Bhatia,et al. On some perturbation inequalities for operators , 1988 .

[13] A. Hoffman,et al. The variation of the spectrum of a normal matrix , 1953 .

[14] T. Andô,et al. An inequality for trace ideals , 1980 .

[15] Fuad Kittaneh,et al. Inequalities for the Schatten p-norm II , 1985, Glasgow Mathematical Journal.

[16] G. Stewart. Pertubation bounds for the definite generalized eigenvalue problem , 1979 .

[17] Fuad Kittaneh,et al. Inequalities for the Schattenp-norm. III , 1986 .