unipotent matrix

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。4i7汉语字典

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。4i7汉语字典

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。4i7汉语字典

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]。4i7汉语字典

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。4i7汉语字典

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。4i7汉语字典

On Nilpotent Matrices over Idempotent and Right-sided Quantale;幂等右侧Quantale上的幂零矩阵4i7汉语字典

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。4i7汉语字典

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4i7汉语字典

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4i7汉语字典

Tripotency of Linear Combinations of Tripotent Matrices三次幂等矩阵的线性组合的三次幂等性4i7汉语字典

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4i7汉语字典

The Properties of Generalized Schur Complement for Partitioned Idempotent Matrix分块幂等矩阵广义Schur补的性质4i7汉语字典

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4i7汉语字典

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。4i7汉语字典

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4i7汉语字典

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。4i7汉语字典

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4i7汉语字典

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4i7汉语字典

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4i7汉语字典

On Idempotent-Hermite Matrices;关于幂等Hermite矩阵的研究4i7汉语字典

Idempotent - Hermite Matrix and Decomposition of Matrices;幂等的Hemite矩阵与矩阵的分解4i7汉语字典

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4i7汉语字典

Estimation of the Idempotent Index Based on AFS Structures;基于AFS结构矩阵的幂等指数估计4i7汉语字典

Linear Operators Preserving Idempotent on 2×2 Matrix Spaces;2×2矩阵空间上保幂等的线性算子4i7汉语字典

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4i7汉语字典

2~n Idempotency of the Hermitian part of a complex matrix复矩阵Hermitian部分的2~n次幂等性4i7汉语字典