کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4598892 1631110 2015 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Generic properties and a criterion of an operator norm
ترجمه فارسی عنوان
خصوصیات عمومی و معیار یک هنجار اپراتور
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

In this paper, we carefully examine the structure of the gradient of an operator norm on a finite-dimensional matrix space. In particular, we derive concise and useful representations for an operator norm and its subgradient, which refine existing results in this area of study. We further use the derived representations to formulate and prove a criterion of an operator norm, the first of its kind, to the best of our knowledge. It essentially states that a matrix norm is an operator norm if and only if the set of its gradients is the set of the outer products of vectors from each pair of the Cartesian product of two vector sets. We also provide several handy tests, based on this criterion, which in certain cases help to determine whether a matrix norm is an operator norm or not. In addition, we generalize our theoretical developments to higher dimensions, i.e. for injective norms on tensor spaces.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 485, 15 November 2015, Pages 1–20
نویسندگان
, ,