کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602660 1336933 2009 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
چکیده انگلیسی

Let Mn+ be the set of entrywise nonnegative n×nn×n matrices. Denote by r(A)r(A) the spectral radius (Perron root) of A∈Mn+. Characterization is obtained for maps f:Mn+→Mn+ such that r(f(A)+f(B))=r(A+B)r(f(A)+f(B))=r(A+B) for all A,B∈Mn+. In particular, it is shown that such a map has the formA↦S-1ASorA↦S-1AtrS,for some S∈Mn+ with exactly one positive entry in each row and each column. Moreover, the same conclusion holds if the spectral radius is replaced by the spectrum or the peripheral spectrum. Similar results are obtained for maps on the set of n×nn×n nonnegative symmetric matrices. Furthermore, the proofs are extended to obtain analogous results when spectral radius is replaced by the numerical range, or the spectral norm. In the case of the numerical radius, a full description of preservers of the sum is also obtained, but in this case it turns out that the standard forms do not describe all such preservers.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 430, Issue 7, 1 April 2009, Pages 1739–1761
نویسندگان
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