کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9500054 1646772 2018 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the connectedness of spectral sets and irreducibility of spectral cones in Euclidean Jordan algebras
ترجمه فارسی عنوان
بر روی همبستگی مجموعه های طیفی و غیر قابل انعطاف مخروط طیفی در جغرافیای اقلیدسی اردن
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
Let V be a Euclidean Jordan algebra of rank n. A set E in V is said to be a spectral set if there exists a permutation invariant set Q in Rn such that E=λ−1(Q), where λ:V→Rn is the eigenvalue map that takes x∈V to λ(x) (the vector of eigenvalues of x written in the decreasing order). If the above Q is also a convex cone, we say that E is a spectral cone. This paper deals with connectedness and arcwise connectedness properties of spectral sets. By relying on the result that in a simple Euclidean Jordan algebra, every eigenvalue orbit [x]:={y:λ(y)=λ(x)} is arcwise connected, we show that if a permutation invariant set Q is connected (arcwise connected), then λ−1(Q) is connected (respectively, arcwise connected). A related result is that in a simple Euclidean Jordan algebra, every pointed spectral cone is irreducible.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 559, 15 December 2018, Pages 181-193
نویسندگان
, ,