## Abstract

Let A and C be square complex matrices of size n, the C-determinantal range of A is the subset of the complex plane {det(A-UC^{U∗}):U^{U∗}=_{In}}. If A, C are both Hermitian matrices, then by a result of Fiedler (1971) [11] this set is a real line segment. In our paper we study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two well-known results on this topic. The first result is due to Li concerning the C-numerical range of a Hermitian matrix, see Condition 5.1 (a) in Li, (1994) [20]. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et al. (2008) [21], Theorem 3.3).

Original language | English |
---|---|

Pages (from-to) | 86-94 |

Number of pages | 9 |

Journal | Applied Mathematics and Computation |

Volume | 275 |

DOIs | |

State | Published - 15 Feb 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2015 Elsevier Inc. All rights reserved.

## Keywords

- C-determinantal range
- C-numerical range
- Marcus-Oliveira conjecture
- Real sets
- σ-points