Utilize este identificador para referenciar este registo:
https://hdl.handle.net/10316/4662
Título: | The Marcus-de Oliveira conjecture, bilinear forms, and cones | Autor: | Kovačec, Alexander | Data: | 1999 | Citação: | Linear Algebra and its Applications. 289:1-3 (1999) 243-259 | Resumo: | The well-known determinantal cinjecture of de Oliveira and Marcus (OMC) confines the determinant det (X + Y) of the sum of normaln × n matricesX,Y to a certain region in the complex plane. Even the subconjecture obtained by specializing it ton = 4,X Hermitian andY normal is still open. We view the subconjecture as a special case of an assertion concerning a certain family of bilinear forms ofR16 ×C16 and give a method that may prove useful for establishing it for many of such matrix pairs, independent of their spectrum; in particular we apply it successfully in the case of a prominent unitary similarity of Drury's threatening OMC. Unfortunately we find the assertion, extended naturally to pairs of complex arguments to be false and the ideas outlined inapplicable for the general OMC(n=4) case. We also report on some computer experiments, formulate OMC(n=4) as a statement about cones, and find it would be implied by establishing the emptiness of certain semialgebraic sets defined by systems of quadratic and linear relations. | URI: | https://hdl.handle.net/10316/4662 | Direitos: | openAccess |
Aparece nas coleções: | FCTUC Matemática - Artigos em Revistas Internacionais |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
---|---|---|---|---|
file496995e38a2649ffb25e7ff0ec47820c.pdf | 2.02 MB | Adobe PDF | Ver/Abrir |
Visualizações de página 50
485
Visto em 16/jul/2024
Downloads
58
Visto em 16/jul/2024
Google ScholarTM
Verificar
Todos os registos no repositório estão protegidos por leis de copyright, com todos os direitos reservados.