کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5773290 | 1631073 | 2017 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On complex matrix scalings of extremal permanent
ترجمه فارسی عنوان
در مقیاس های ماتریکس پیچیده از دائمی افراطی
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
A doubly quasi-stochastic (DQS) matrix is said to be maximally (minimally) scaled if it cannot be diagonally scaled to another doubly quasi-stochastic matrix with larger (smaller) permanent. Motivated by a connection to the geometric measure of entanglement of certain symmetric states, we offer a series of results on the structures of the sets of nÃn maximally scaled (MaxScn) and minimally scaled (MinScn) DQS matrices. In particular, we offer a characterization of the set of nÃn maximally scaled matrices, and use this characterization to show that these matrices form a convex set and that the nÃn identity matrix is the element of MaxScn with smallest permanent. We then show that real DQS matrices in MaxScn or MinScn must satisfy certain spectral properties, and use these properties to show that all positive definite doubly stochastic matrices are minimally scaled. We finish with a bound on the permanent of any real matrix or Abelian group matrix in MinScn.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 522, 1 June 2017, Pages 111-126
Journal: Linear Algebra and its Applications - Volume 522, 1 June 2017, Pages 111-126
نویسندگان
George Hutchinson,