کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11598631 | 1337268 | 2019 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On Cartesian product of Euclidean distance matrices
ترجمه فارسی عنوان
بر روی محصول دکارتی ماتریس فاصله اقلیدس
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
If AâRmÃm and BâRnÃn, we define the product AâB as AâB=AâJn+JmâB, where â denotes the Kronecker product and Jn is the nÃn matrix of all ones. We refer to this product as the Cartesian product of A and B since if D1 and D2 are the distance matrices of graphs G1 and G2 respectively, then D1âD2 is the distance matrix of the Cartesian product G1â¡G2. We study Cartesian products of Euclidean distance matrices (EDMs). We prove that if A and B are EDMs, then so is the product AâB. We show that if A is an EDM and U is symmetric, then AâU is an EDM if and only if U=cJn for some c. It is shown that for EDMs A and B, AâB is spherical if and only if both A and B are spherical. If A and B are EDMs, then we derive expressions for the rank and the Moore-Penrose inverse of AâB. In the final section we consider the product AâB for arbitrary matrices. For AâRmÃm,BâRnÃn, we show that all nonzero minors of AâB of order m+nâ1 are equal. An explicit formula for a nonzero minor of order m+nâ1 is proved. The result is shown to generalize the familiar fact that the determinant of the distance matrix of a tree on n vertices does not depend on the tree and is a function only of n.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 562, 1 February 2019, Pages 135-153
Journal: Linear Algebra and its Applications - Volume 562, 1 February 2019, Pages 135-153
نویسندگان
Ravindra B. Bapat, Hiroshi Kurata,