Three observations on the determinantal range

• Autor(es): Bebiano, N. ; Soares, G.
• Data: 2005
• Identificador Persistente: http://hdl.handle.net/10316/4629
• Origem: Estudo Geral - Universidade de Coimbra
• Assunto(s): Keywords; Determinantal range; Cross ratio; Linear preserver
• Tipo de Documento: Artigo
• Idioma: Inglês

Descrição

Let A, C [set membership, variant] Mn, the algebra of n × n complex matrices. The set of complex numbersis the C-determinantal range of A. In this note, it is proved that [Delta]C(A) is an elliptical disc for A, C [set membership, variant] M2. A necessary and sufficient condition for [Delta]C(A) to be a line segment is given when A and C are normal matrices with pairwise distinct eigenvalues. The linear operators L that satisfy the linear preserver property [Delta]C(A) = [Delta]C(L(A)), for all A, C [set membership, variant] Mn, are characterized. http://www.sciencedirect.com/science/article/B6V0R-4D0Y71M-2/1/682f05b81ddaa6914f85e6ba5e02f63b