共查询到20条相似文献,搜索用时 15 毫秒
1.
Yi-jia Tan 《Czechoslovak Mathematical Journal》2006,56(2):299-316
In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice L are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set F
n
(L) of all n × n fully indecomposable matrices as a subsemigroup of the semigroup H
n
(L) of all n × n Hall matrices over the lattice L are given. 相似文献
2.
By a theorem of Levitzki, we prove that a generalized strongly nilpotent matrix is similar to a upper triangular matrix with zero diagonal by a scalar matrix, which generalizes a recent result by van den Essen and Hubbers. We also show that a special case of a conjecture of Connell and Zweibel is true. 相似文献
3.
Invertible matrices over distributive lattices 总被引:3,自引:0,他引:3
L. A. Skornyakov 《Siberian Mathematical Journal》1986,27(2):289-292
4.
Nieminen Juhani 《manuscripta mathematica》1972,7(1):13-21
Let L be a distributive lattice characterized by a ternary operation (, ,), where (a,b,c)=(ab)(bc)(ac)=(ab)(ac)(bc), a,b,cL. The note considers convex sublattices of L, called generalized ideals of L generated by the operation (, ,). Some remarks have been stated about the graph of a distributive lattice. 相似文献
5.
V. E. Marenich 《Journal of Mathematical Sciences》2010,164(2):260-271
Characteristics for lattice matrices to be prime and existence criteria for prime matrices over distributive lattices are obtained. 相似文献
6.
David Dol?an 《Linear algebra and its applications》2009,430(1):271-2258
In this paper, we characterize invertible matrices over an arbitrary commutative antiring S with 1 and find the structure of GLn(S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent n×n matrix over an entire antiring can be written as a sum of ⌈log2n⌉ square-zero matrices and also find the necessary number of square-zero summands for an arbitrary trace-zero matrix to be expressible as their sum. 相似文献
7.
Some aspects of intuitionistic fuzzy sets 总被引:1,自引:0,他引:1
Ronald R. Yager 《Fuzzy Optimization and Decision Making》2009,8(1):67-90
We first discuss the significant role that duality plays in many aggregation operations involving intuitionistic fuzzy subsets.
We then consider the extension to intuitionistic fuzzy subsets of a number of ideas from standard fuzzy subsets. In particular
we look at the measure of specificity. We also look at the problem of alternative selection when decision criteria satisfaction
is expressed using intuitionistic fuzzy subsets. We introduce a decision paradigm called the method of least commitment. We
briefly look at the problem of defuzzification of intuitionistic fuzzy subsets. 相似文献
8.
9.
Mahbobeh Hosseinyazdi 《Journal of Global Optimization》2008,41(2):283-298
In this paper we give a necessary and sufficient condition for existence of minimal solution(s) of the linear system A * X ≥ b where A, b are fixed matrices and X is an unknown matrix over a lattice. Next, an algorithm which finds these minimal solutions over a distributive lattice is
given. Finally, we find an optimal solution for the optimization problem min {Z = C * X | A * X ≥ b} where C is the given matrix of coefficients of objective function Z.
This research was completed while the author was a visitor of the Center for Informatics and Applied Optimization, University
of Ballarat, Ballarat, Australia. 相似文献
10.
In this short note, we prove that a complete lattice is a generalized completely distributive lattice if and only if its order dual is a hypercontinuous lattice. 相似文献
11.
12.
Soft set theory was originally proposed by Molodtsov as a general mathematical tool for dealing with uncertainty in 1999. Recently, researches of decision making based on soft sets have got some progress, but few people consider multi-experts situation. As such, this paper discusses multi-experts group decision making problems. Firstly, we give a concept of intuitionistic fuzzy soft matrix (IFSM) and prove some relevant properties of IFSM. Then, an adjustable approach is presented by means of median level soft set and p-quantile level soft set for dealing with decision making problems based on IFSM. Thirdly, we study aggregation methods of IFSM, give two kinds of aggregation operators and methods that how to determine experts’ weights under different situation with programming models, four corresponding algorithms have been proposed, too. Finally, a practical example has been demonstrated the reasonability and efficiency of these new algorithms. 相似文献
13.
14.
15.
We compute the greatest solutions of systems of linear equations over a lattice (P, ≤). We also present some applications of the results obtained to lattice matrix theory. Let (P, ≤) be a pseudocomplemented lattice with
and
and let A = ‖a
ij
‖
n×n
, where a
ij
∈ P for i, j = 1,..., n. Let A* = ‖a
ij
′
‖
n×n
and
for i, j = 1,..., n, where a* is the pseudocomplement of a ∈ P in (P, ≤). A matrix A has a right inverse over (P, ≤) if and only if A · A* = E over (P, ≤). If A has a right inverse over (P, ≤), then A* is the greatest right inverse of A over (P, ≤). The matrix A has a right inverse over (P, ≤) if and only if A is a column orthogonal over (P, ≤). The matrix D = A · A* is the greatest diagonal such that A is a left divisor of D over (P, ≤).
Invertible matrices over a distributive lattice (P, ≤) form the general linear group GL
n
(P, ≤) under multiplication. Let (P, ≤) be a finite distributive lattice and let k be the number of components of the covering graph Γ(join(P,≤) −
, ≤), where join(P, ≤) is the set of join irreducible elements of (P, ≤). Then GL
a
(P, ≤) ≅ = S
n
k
.
We give some further results concerning inversion of matrices over a pseudocomplemented lattice.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 3, pp. 139–154, 2005. 相似文献
16.
17.
We show that any complex singular square matrix T is a product of two nilpotent matrices A and B with rank A = rank B = rank T except when T is a 2×2 nilpotent matrix of rank one. 相似文献
18.
19.
20.
We study matrices over general rings which are sums of nilpotent matrices. We show that over commutative rings all matrices with nilpotent trace are sums of three nilpotent matrices. We characterize 2-by-2 matrices with integer entries which are sums of two nilpotents via the solvability of a quadratic Diophantine equation. Some exemples in the case of matrices over noncommutative rings are given. 相似文献