کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4601882 1336908 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A link between the Perron–Frobenius theorem and Perron’s theorem for difference equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A link between the Perron–Frobenius theorem and Perron’s theorem for difference equations
چکیده انگلیسی

Let An,n∈NAn,n∈N, be a sequence of k×kk×k matrices which converge to a matrix A   as n→∞n→∞. It is shown that if xn,n∈Nxn,n∈N, is a sequence of nonnegative nonzero vectors such thatxn+1=Anxn,n∈N, then ρ=limn→∞‖xn‖n is an eigenvalue of the limiting matrix A with a nonnegative eigenvector. This result implies the weak form of the Perron–Frobenius theorem and for the class of nonnegative solutions it improves the conclusion of a Perron type theorem for difference equations.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 434, Issue 2, 15 January 2011, Pages 490–500
نویسندگان
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