کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
403125 | 677053 | 2013 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Determinantal representations of hyperbolic plane curves: An elementary approach
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
هوش مصنوعی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In 2007, Helton and Vinnikov proved that every hyperbolic plane curve has a definite real symmetric determinantal representation. By allowing for Hermitian matrices instead, we are able to give a new proof that relies only on the basic intersection theory of plane curves. We show that a matrix of linear forms is definite if and only if its co-maximal minors interlace its determinant and extend a classical construction of determinantal representations of Dixon from 1902. Like the Helton–Vinnikov theorem, this implies that every hyperbolic region in the plane is defined by a linear matrix inequality.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 57, October 2013, Pages 48–60
Journal: Journal of Symbolic Computation - Volume 57, October 2013, Pages 48–60
نویسندگان
Daniel Plaumann, Cynthia Vinzant,