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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

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
Journal: Linear Algebra and its Applications - Volume 428, Issues 11–12, 1 June 2008, Pages 2536-2548