| GCD和GCUD矩阵行列式的一个不等式（英） |
| |
| 作者姓名： | PENTTI Haukkanen JUHA SIllanpaa |
| |
| 作者单位： | Dept. of Math. Sci，University of Tampers P.O.Box 607，FIN-33101 Tampere，Finland |
| |
| 摘 要： | Let S = {x1, x2,..., xn} be a set of distinct positive integers. The n x n matrix (S) whose i, j-entry is the greatest common divisor (xi, xj) of xi and xj is called the GCD matrix on S. A divisor d of x is said to be a unitary divisor of x if (d, x/d) = 1. The greatest common unitary divisor (GCUD) matrix (S**) is defined analogously. We show that if S is both GCD-closed and GCUD-closed, then det(S**) ≥ det(S), where the equality holds if and Only if (S**) = (S).
|
| 关 键 词： | Srith′s determinant GCD matrix unitary analogue inequality. |
| 收稿时间： | 1997/7/15 0:00:00 |
An Inequality for the Determinant of the GCD Matrix and the GCUD Matrix |
| |
| PENTTI Haukkanen,JUHA SIllanpaa.An Inequality for the Determinant of the GCD Matrix and the GCUD Matrix[J].Journal of Mathematical Research with Applications,2000,20(2):181-186. |
| |
| Authors: | PENTTI Haukkanen and JUHA SIllanpaa |
| |
| Institution: | Dept. of Math. Sci., University of Tampere P.O.Box 607, FIN-33101 Tampere, Finland |
| |
| Abstract: | Let S ＝ {x1, x2,...,xn} be a set of distinct positive integers. The n × nmatrix (S) whose i,j-entry is the greatest common divisor (xi, xj) of xi and xj is called the GCD matrix on S. A divisor d of x is said to be a unitary divisor of x if (d, x/d)=1.The greatest common unitary divisor (GCUD) matrix (S**) is defined analogously. We show that if S is both GCD-closed and GCUD-closed, then det(S**)≥det(S), where the equality holds if and only if (S**) = (S). |
| |
| Keywords: | Srith's determinant GCD matrix unitary analogue inequality |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |
