کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602340 1631167 2008 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Geometrical properties of the Frobenius condition number for positive definite matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Geometrical properties of the Frobenius condition number for positive definite matrices
چکیده انگلیسی

We study the geometrical properties of the Frobenius condition number on the cone of symmetric and positive definite matrices. This number, related to the cosine of the angle between a given matrix and its inverse, is equivalent to the classical 2-norm condition number, but has a direct and natural geometrical interpretation. In particular we establish bounds for the ratio between the angle that a matrix forms with the identity ray and the angle that the inverse of that matrix forms with the identity ray. These bounds allow us to establish new lower bounds for the condition number, that only require the trace and the Frobenius norm of the matrix.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issues 8–9, 16 October 2008, Pages 2089-2097