1) power matrices
可幂矩阵
4) nilpotent matrix
幂零矩阵
1.
In this paper,the concept of nilpotent matrix is used to discuss some characters of the nilpotent matrix in general number field.
利用幂零矩阵的概念,在一般数域上讨论了幂零矩阵的一些性质,给出了矩阵是幂零矩阵的一个充要条件,最后利用幂零线性变换的概念,在一般数域上讨论了幂零线性变换一定存在一组基使其在这组基下的矩阵是若当形矩阵,从而给出幂零矩阵的若当标准形。
2.
However, the properties of nilpotent matrix have not been much explored although its definition is given in discussing the multiplication of matrix.
在高等代数中矩阵是研究问题很重要的工具,在讨论矩阵的乘法运算时给出了幂零矩阵的定义,但对其性质研究很少。
3.
This paper is derived to the study of the equation X~m=A where A is a n×n nilpotent matrix with 2≤m∈N.
主要研究当A是幂零矩阵时,方程Xm=A的性质。
5) 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。
6) nilpotent matrices
幂零矩阵
1.
On Nilpotent Matrices over Idempotent and Right-sided Quantale;
幂等右侧Quantale上的幂零矩阵
2.
In this paper,we characterize isotropy subgroups of Jordan normal form of 3-nilpotent matrices under the conjugate action of GLn(F).
刻画了3-幂零矩阵的Jordan标准型在GLn(F)共轭作用下的迷向子群的结构。
3.
This paper devotes to an approach to nilpotent matrices and gives a classification theorem on lower dimensional nilpotent algebras.
讨论了幂零矩阵的性质 ,给出了低维幂零代数的分
补充资料：彻幂
1.见"彻幂"。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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