Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/15348
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 σ-points 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 |
URI: | http://hdl.handle.net/10773/15348 |
DOI: | 10.1016/j.amc.2015.11.042 |
ISSN: | 0096-3003 |
Appears in Collections: | CIDMA - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
GutermanLemosSoares.pdf | Preprint | 349.35 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.