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Title: On the C-determinantal range for special classes of matrices
Author: Guterman, Alexander
Lemos, Rute
Soares, Graça
Keywords: C-determinantal range
C-numerical range
Marcus-Oliveira conjecture
Real sets
Issue Date: 15-Feb-2016
Publisher: Elsevier
Abstract: Let A and C be square complex matrices of sizen, 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 theC-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).
Peer review: yes
DOI: 10.1016/j.amc.2015.11.042
ISSN: 0096-3003
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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