کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603503 1631179 2007 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A generalized eigenvalue problem in the max algebra
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A generalized eigenvalue problem in the max algebra
چکیده انگلیسی

We consider the generalized eigenvalue problemA⊗x=λB⊗x,x⩾0,x≠0,where A and B are (entrywise) nonnegative n × n matrices, and the “max” product ⊗ satisfies(A⊗x)i≔maxm=1naimxm.The case B = I has been studied by several authors, and for irreducible (e.g., positive) A there is exactly one eigenvalue λ in the above “max” sense.The generalized problem is different, and for example neither existence nor uniqueness of eigenvalues is guaranteed, even for 2 × 2 positive matrices A and B, which can be analysed by graphical methods. For general n, existence and uniqueness are discussed by different methods including degree theory.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 422, Issues 2–3, 15 April 2007, Pages 360–371
نویسندگان
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