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Search Results: 1 - 10 of 302065 matches for " <br>idempotent matrix "
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Linear Operators Preserving Idempotent Matrices Over Division Rings

科学通报(英文版) , 1993,
Abstract:
Matrix structures over connected rings

科学通报(英文版) , 1996,
Abstract:
矩阵的两个幂等矩阵组合的可逆性
Invertibility of the combination of two idempotent matrices which products is idempotent matrix

曹元元,左可正,熊 瑶
CAO Yuanyuan
,ZUO Kezheng,XIONG Yao

- , 2017,
Abstract: 利用幂等矩阵的性质及两个幂等矩阵的和与差的可逆性,研究了两个幂等矩阵P,Q在条件(PQ)2=PQ下,它们的组合T=aP+bQ+cPQ+dQP+ePQP+fQPQ+g(QP)2,(a,b,c,d,e,f,g∈?,ab≠0)的可逆性,并给出它的求逆公式.
两个幂等矩阵线性组合的Drazin逆
Drazin inverse of linear combination of two idempotent matrices

曹秋红,谢 涛,左可正
CAO Qiuhong
,XIE Tao,ZUO Kezheng

- , 2018,
Abstract: 利用幂等矩阵的性质及Drazin逆的定义, 证明了两个不同的非零幂等矩阵P,Q的线性组合aP+bQ(其中a,b∈,a,b≠0)在条件mP=m下存在Drazin逆, 并且给出其Drazin 逆的计算公式.
(u,v)幂等矩阵与本质(m,l)幂等矩阵
(u,v)-idempotent matrices and essential (m,l)-idempotent matrices

林志兴,杨忠鹏,陈梅香,陈智雄,陈少琼
福州大学学报(自然科学版) , 2015, DOI: 10.7631/issn.1000-2243.2015.03.0311
Abstract: 证明了(u,v)幂等矩阵与本质(m,l)幂等矩阵的互相确定关系,由此给出了求(u,v)幂等矩阵的Jordan标准形的方法,这种方法不依赖通常的求Jordan标准形的算法,只涉及到矩阵方幂的秩和u-v次单位根εi所确定的矩阵秩最后得到以矩阵秩为基本工具的,判定(u1,v1)幂等矩阵与(u2,v2)幂等矩阵相似的充分必要条件.
It has been proved that (u,v)-idempotent matrices and essential (m,l)-idempotent matrices can be determined by each other. Then it gives us a method to work out the Jordan canonical form of a (u,v)-idempotent matrix,independently on the usual method of the Jordan canonical form,only referring to the ranks of matrix powers and u-v-th unity roots εi . By using ranks of matrices as a basic tool,it also obtains some sufficient and necessary conditions for a (u1,v1)-idempotent matrix to be similar to a (u2,v2)-idempotent one
Idempotent and compact matrices on linear lattices: a survey of some lattice results and related solutions of finite relational equations
Fortunata Liguori,Giulia Martini,Salvatore Sessa
International Journal of Mathematics and Mathematical Sciences , 1993, DOI: 10.1155/s0161171293000365
Abstract: After a survey of some known lattice results, we determine the greatest idempotent (resp. compact) solution, when it exists, of a finite square rational equation assigned over a linear lattice. Similar considerations are presented for composite relational equations.
体上一类具有幂等子块的分块矩阵的群逆
卜长江,郑兰,凌焕章
哈尔滨工程大学学报 , 2009, DOI: 10.3969/j.issn.1006-7043.2009.10.019
Abstract: 设K是一个体, K_(m×n)表示m×n上所有K矩阵的集合.对矩阵A∈K 若存在矩阵X∈K_(n×n)使AXA=A,XAX=X,AX=XA,则称X为A的群逆.研究分块矩阵广义逆的表达式是矩阵广义逆理论中研究的重要问题.分块矩阵的群逆表达式在奇异微分和差分方程、马尔可夫链、迭代方法和密码学等领域有广泛应用.这里给出了体上分块矩阵[ABB0](A,B∈K_(n×n),B~2=B,((I-B)A)~#存在)的群逆的存在性及表示形式.
First order linear ordinary differential equations in associative algebras
Gordon Erlebacher,Garrret E. Sobczyk
Electronic Journal of Differential Equations , 2004,
Abstract: In this paper, we study the linear differential equation $$ frac{dx}{dt}=sum_{i=1}^n a_i(t) x b_i(t) + f(t) $$ in an associative but non-commutative algebra $mathcal{A}$, where the $b_i(t)$ form a set of commuting $mathcal{A}$-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.
矩阵线性组合幂等性及立方幂等性的一些结论
卜长江,李娜,孙艳玲
哈尔滨工程大学学报 , 2009, DOI: 10.3969/j.issn.1006-7043.2009.12.021
Abstract: 研究幂等矩阵和立方幂等矩阵的线性组合在矩阵理论和统计学中具有重要的意义.设A、B是2个n×n的复矩阵,令P=_(c1)A+_(c2)B,其中c_1、c_2为非零复数.该文在AB=BA的条件下分别给出:当A分别为幂等矩阵和立方幂等矩阵,B为任意矩阵时,线性组合P分别为幂等的和立方幂等的充分必要条件.并且利用以上结果直接得出下面的结论:当A为幂等矩阵,B为与A可交换的幂等矩阵或立方幂等矩阵时,P是幂等矩阵的充分必要条件;当A和B为可交换的立方幂等矩阵时,P是立方幂等矩阵的充分必要条件.
关于某些特殊分块矩阵的群逆
卜长江,郑金山,赵杰梅
哈尔滨工程大学学报 , 2009, DOI: 10.3969/j.issn.1006-7043.2009.09.020
Abstract: 分块矩阵的广义逆不仅在数学理论上有广泛研究而且在自动控制、系统理论、概率统计、数学规划等领域有着广泛的实际研究背景.该文对形如[A B/C 0]分块矩阵的群逆的表达式问题进行了研究.设P是复数域上的幂等阵.令矩阵A,B,C取自集合{P,PP~*,PP~*P },则可以得到27个形如[A B/C 0]的分块矩阵.给出了这27个分块矩阵群逆的存在性与表示形式.
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