Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/4598
DC Field | Value | Language |
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dc.contributor.author | Kovačec, Alexander | - |
dc.contributor.author | Bebiano, Natália | - |
dc.contributor.author | Providência, João da | - |
dc.date.accessioned | 2008-09-01T11:35:00Z | - |
dc.date.available | 2008-09-01T11:35:00Z | - |
dc.date.issued | 2007 | en_US |
dc.identifier.citation | Linear Algebra and its Applications. 426:1 (2007) 96-108 | en_US |
dc.identifier.uri | https://hdl.handle.net/10316/4598 | - |
dc.description.abstract | Let A be a complex n×n matrix and let SO(n) be the group of real orthogonal matrices of determinant one. Define [Delta](A)={det(AoQ):Q[set membership, variant]SO(n)}, where o denotes the Hadamard product of matrices. For a permutation [sigma] on {1,...,n}, define It is shown that if the equation z[sigma]=det(AoQ) has in SO(n) only the obvious solutions (Q=([epsilon]i[delta][sigma]i,j), [epsilon]i=±1 such that [epsilon]1...[epsilon]n=sgn[sigma]), then the local shape of [Delta](A) in a vicinity of z[sigma] resembles a truncated cone whose opening angle equals , where [sigma]1, [sigma]2 differ from [sigma] by transpositions. This lends further credibility to the well known de Oliveira Marcus Conjecture (OMC) concerning the determinant of the sum of normal n×n matrices. We deduce the mentioned fact from a general result concerning multivariate power series and also use some elementary algebraic topology. | en_US |
dc.description.uri | http://www.sciencedirect.com/science/article/B6V0R-4NJG44V-3/1/29cc71d6352bcfea422c3dc7beebcbce | en_US |
dc.format.mimetype | aplication/PDF | en |
dc.language.iso | eng | eng |
dc.rights | openAccess | eng |
dc.subject | Determinantal range | en_US |
dc.subject | Hadamard product | en_US |
dc.subject | Power series | en_US |
dc.subject | Corners | en_US |
dc.subject | Oliveira Marcus Conjecture | en_US |
dc.title | On the corners of certain determinantal ranges | en_US |
dc.type | article | en_US |
dc.identifier.doi | 10.1016/j.laa.2007.04.010 | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
item.grantfulltext | open | - |
item.fulltext | Com Texto completo | - |
item.languageiso639-1 | en | - |
crisitem.author.dept | Faculty of Sciences and Technology | - |
crisitem.author.parentdept | University of Coimbra | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0003-4215-3067 | - |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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filed541298c5cf9420dab12c428ac602d3a.pdf | 233.06 kB | Adobe PDF | View/Open |
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