## Abstract

Let A_{0} be a transformation on a finite dimensional Hilbert space which is self-adjoint in an indefinite scalar product generated by G_{0} (G^{*}_{0} and invertible). The spectrum of A_{0} is real when A_{0} is G_{0}-strongly definitizable. The problems considered here concern the number of real eigenvalues of a G-self-adjoint transformation A where A and G are low rank perturbations of A_{0} and G_{0}. A notion called the "order of neutrality" of A with respect to G is introduced which is relevant to this problem area. Using linearization as well as direct methods, results are obtained concerning self-adjoint matrix polynomials which are low rank perturbationsof (suitably defined) definitizable matrix polynomials. Applications are made to quadratic matrix polynomials arising in the study of damped systems and gyroscopic systems.

Original language | English |
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Pages (from-to) | 3-29 |

Number of pages | 27 |

Journal | Linear Algebra and Its Applications |

Volume | 197-198 |

Issue number | C |

DOIs | |

State | Published - 1994 |

### Bibliographical note

Funding Information:*The work of these authors was supported in part by grants from the Natural Sciences and

Funding Information:

Engineering Research Council of Canada and the Israel Ministry of Science, respectively.

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics