On the C-determinantal range for special classes of matrices

Alexander Guterman, Rute Lemos, Graça Soares

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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-UCU∗):UU∗=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 languageEnglish
Pages (from-to)86-94
Number of pages9
JournalApplied Mathematics and Computation
Volume275
DOIs
StatePublished - 15 Feb 2016
Externally publishedYes

Bibliographical note

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

Keywords

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

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