کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602371 1631170 2008 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bidiagonal decompositions of oscillating systems of vectors
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Bidiagonal decompositions of oscillating systems of vectors
چکیده انگلیسی

We establish necessary and sufficient conditions, in the language of bidiagonal decompositions, for a matrix V to be an eigenvector matrix of a totally positive matrix. Namely, this is the case if and only if V and V-T are lowerly totally positive. These conditions translate into easy positivity requirements on the parameters in the bidiagonal decompositions of V and V-T. Using these decompositions we give elementary proofs of the oscillating properties of V. In particular, the fact that the jth column of V has j-1 changes of sign. Our new results include the fact that the Q matrix in a QR decomposition of a totally positive matrix belongs to the above class (and thus has the same oscillating properties).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issues 11–12, 1 June 2008, Pages 2536-2548