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。
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。
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。
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]。
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。
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。
On Nilpotent Matrices over Idempotent and Right-sided Quantale;
幂等右侧Quantale上的幂零矩阵
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。
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
On Characteristics of(m,l)Rank-idempotent Matrix and(m,l)Idempotent Matrix
(m,/)秩幂等矩阵和(m,/)幂等矩阵的特性研究
Tripotency of Linear Combinations of Tripotent Matrices
三次幂等矩阵的线性组合的三次幂等性
Some Conditions of Nonsingularity of Linear Combinations of Idempotent Matrices;
幂等矩阵线性组合可逆性的若干条件
The Properties of Generalized Schur Complement for Partitioned Idempotent Matrix
分块幂等矩阵广义Schur补的性质
The Researches on the Zero Matrices and Identity Matrices for Linear Expression of Idempotent Matrices
幂等矩阵线性组合表出零矩阵和单位矩阵的研究
Nine equivalent conditions of real idempotent matrix are given and proved, and one equivalent condition of real symmetric idempotent matrix is also given in this paper.
给出并证明了实幂等矩阵的九个等价条件,以及实对称幂等矩阵的一个等价条件。
Some Proofs of One Proposition about Rank of Matrix and Its Generalization
关于幂等矩阵秩的一个命题的证明和推广
This paper gives a new conclusion about the expression of｛1｝ inverse of aggregate A｛1｝ by using power equal matrix, full rank decomposition and the property of｛1｝ inverse.
利用幂等矩阵、满秩分解以及{}逆的性质,得到{}逆的集合A{}表征新结论。
Using Normal Form of Idempotent Matrices of Degree Three over Z_(p~k) to Construct Cartesian Authentication Codes;
利用Z_（p~k）上三次幂等矩阵的标准形构作Cartesian认证码
Using Normal Form of Idempotent Matrices over Finite Fields to Construct Authentication Codes with Arbitration
利用有限域上幂等矩阵的标准型构造带仲裁的认证码
The generalized inverse of two idempotent matrices and their product under the similar transformation over a local ring
局部环上两个同阶幂等矩阵及其积在同一相似变换下的广义逆
On Idempotent-Hermite Matrices;
关于幂等Hermite矩阵的研究
Idempotent - Hermite Matrix and Decomposition of Matrices;
幂等的Hemite矩阵与矩阵的分解
Some results on idempotency and tripotency of linear combinations of matrices
矩阵线性组合幂等性及立方幂等性的一些结论
Estimation of the Idempotent Index Based on AFS Structures;
基于AFS结构矩阵的幂等指数估计
Linear Operators Preserving Idempotent on 2×2 Matrix Spaces;
2×2矩阵空间上保幂等的线性算子
Maps Preserving Tripotent on Several Classes of Matrix Spaces over Field
域上几类矩阵空间保立方幂等的映射
2~n Idempotency of the Hermitian part of a complex matrix
复矩阵Hermitian部分的2~n次幂等性
