## Abstract

For n × n complex matrices A, C and H, where H is non-singular Hermitian, the Krein space C-numerical range of A induced by H is the subset of the complex plane given by {Tr(CU ^{[*]} AU):U ^{−1} =U ^{[*]} } with U ^{[*]} =H ^{−1} U ^{*} H the H-adjoint matrix of U. We revisit several results on the geometry of Krein space C-numerical range of A and in particular we obtain a condition for the Krein space C-numerical range to be a subset of the real line.

Original language | English |
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Pages (from-to) | 258-269 |

Number of pages | 12 |

Journal | Applied Mathematics and Computation |

Volume | 352 |

DOIs | |

State | Published - 1 Jul 2019 |

Externally published | Yes |

### Bibliographical note

Funding Information:The work of the first author is supported by the grant RSF 17-11-01124. The work of the second author was supported by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA) and the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia) , within the project UID/MAT/0416/2013 . The work of the third author was financed by Portuguese Funds through FCT - Fundação para a Ciência e Tecnologia , within the Project UID/MAT/00013/2013 .

Publisher Copyright:

© 2019 Elsevier Inc.

## Keywords

- Indefininte inner product
- J−Hermitian matrix
- Krein space C-numerical range