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1)  The inverses of GCD and LCM matrices
GCD和LCM幂矩阵的逆矩阵
2)  power GCD matrix
幂GCD矩阵
1.
In this paper,a necessary and sufficient conditions on the gcd closed set S with |S|=4 such that the power GCD matrix(Se)on S divides the power LCM matrix on S in the ring M4(Z) of 4×4 matrices over the integers is proved.
在本文中,我们给出了关于四元gcd封闭集S的充分必要条件,使得在环M4(Z)中,定义在S上的e次幂GCD矩阵(Se)整除e次幂LCM矩阵[Se]。
3)  power LCM matrix
幂LCM矩阵
1.
In this paper,a necessary and sufficient conditions on the gcd closed set S with |S|=4 such that the power GCD matrix(Se)on S divides the power LCM matrix on S in the ring M4(Z) of 4×4 matrices over the integers is proved.
在本文中,我们给出了关于四元gcd封闭集S的充分必要条件,使得在环M4(Z)中,定义在S上的e次幂GCD矩阵(Se)整除e次幂LCM矩阵[Se]。
2.
Shaofang Hong conjectured in 2002 that for a given positive integer t there is a positive integer k(t) depending only on t, such that if n≤k(t), then the power LCM matrix ([x_i, x_j]~t) defined on any gcd-closed set S={x_1,…,x_n} is nonsingular; but for n≥k(t)+1, there exists a gcd-closed set S={x_1,…,x_n} such that the power LCM matrix ([x_i, x_j]~t) on S is singular.
洪绍方在2002年猜想:对于给定的一个正整数t,存在一个仅由t决定的正整数k(t),使得当n≤k(t)时,定义在任意gcd闭集S={x1,…,xn}上的幂LCM矩阵([xi,xj]t)是非奇异的;而当n≥k(t)+1,则存在一个gcd闭集S={x1,…,xn},使得定义在其上的幂LCM矩阵([xi,xj]t)奇异。
3.
In this paper, we showthat for any real number e ≥1 and n ≤7, the power LCM matrix ([x_i,x_j]~e) definedon any gcd-closed set S = {x_1,.
第i 行j 列元素由xi 和xj 的最小公倍数的e次幂[x_i,x_j]~e 构成的n ×n矩阵([x_i,x_j]~e),称为定义在S 上的e次幂LCM矩阵。
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4)  LCM power matrices
LCM幂矩阵
5)  power reciprocal GCD matrix
倒数幂GCD矩阵
6)  GCD matrix
GCD矩阵
1.
It is proved in this paper that if S consists of two relatively prime divisor chains,then the GCD matrix on S divides the LCM matrix on S.
作者证明:若S由两个互素的因子链构成,那么在n阶整数矩阵环中,GCD矩阵(S)整除LCM矩阵[S]。
2.
The n×n matrix whose (i,j)-entry is the greatest common divisor (xi,xj)of xi and xj is called the GCD matrix on S, denoted by (S).
我们称以xi和xj的最大公因子(xi,xj)为(i,j)项的n×n矩阵为定义在集合S上的GCD矩阵,记为(S)。
补充资料：S矩阵
分子式：
CAS号：

性质：简称S-矩阵。在碰撞问题中完全决定相对运动波函数进行为的一种用矩阵形式表征的量。

说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条