کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4602682 | 1336934 | 2007 | 13 صفحه PDF | دانلود رایگان |
Let A be a complex n×n matrix and let SO(n) be the group of real orthogonal matrices of determinant one. Define Δ(A)={det(A∘Q):Q∈SO(n)}, where ∘ denotes the Hadamard product of matrices. For a permutation σ on {1,…,n}, define It is shown that if the equation zσ=det(A∘Q) has in SO(n) only the obvious solutions (Q=(εiδσi,j), εi=±1 such that ε1…εn=sgnσ), then the local shape of Δ(A) in a vicinity of zσ resembles a truncated cone whose opening angle equals , where σ1, σ2 differ from σ 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.
Journal: Linear Algebra and its Applications - Volume 426, Issue 1, 1 October 2007, Pages 96-108