کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4598877 | 1631106 | 2016 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Hourglass alternative and the finiteness conjecture for the spectral characteristics of sets of non-negative matrices
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Recently Blondel, Nesterov and Protasov proved [1,2] that the finiteness conjecture holds for the generalized and the lower spectral radii of the sets of non-negative matrices with independent row/column uncertainty. We show that this result can be obtained as a simple consequence of the so-called hourglass alternative used in [3], by the author and his companions, to analyze the minimax relations between the spectral radii of matrix products. Axiomatization of the statements that constitute the hourglass alternative makes it possible to define a new class of sets of positive matrices having the finiteness property, which includes the sets of non-negative matrices with independent row uncertainty. This class of matrices, supplemented by the zero and identity matrices, forms a semiring with the Minkowski operations of addition and multiplication of matrix sets, which gives means to construct new sets of non-negative matrices possessing the finiteness property for the generalized and the lower spectral radii.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 489, 15 January 2016, Pages 167-185
Journal: Linear Algebra and its Applications - Volume 489, 15 January 2016, Pages 167-185
نویسندگان
Victor Kozyakin,