共查询到20条相似文献,搜索用时 15 毫秒
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OnCompanionBooleanRelationMatricesChaoChongyun(Dept.ofMathUnivofPittsburghPittsburgh,PA15260)WangTianming(Inst.ofMath.Science... 相似文献
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Generalized inverses of Boolean Matrices are defined and the general form of matrices having generalized inverses is determined. Some structure theorems are proved, from which, some known results are obtained as corollaries. An algorithm to compute a generalized inverse of a matrix, when it exists, is given. The existence of various types of g-inverses is also investigated. All the results are obtained first for the {0,1}-Boolean algebra and then extended to an arbitrary Boolean algebra. 相似文献
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No Abstract. February 8, 1999 相似文献
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In this paper, we study some of properties of the min-max compositions of fuzzy matrices and give out a dual theorem (to Theorem 3 of [4]) about the convergence of the power sequence of min-max compositions of fuzzy matrices.AMS Subject Classification (2000) 15A45 06A06 04A72 相似文献
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Jin Bai Kim 《数学研究及应用》1985,5(3):11-13
We give a characterization of a regular Boolean matrix and prove that AB = I Implies that BA = I, where A and B are Boolean matrices whose elements belong to a Boolean algebra of a set with more than two elements. 相似文献
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n -2 integers 2 n -2+2 n -3+2 s, where s=0,1,2,..., n-3, in the interval (2 n -2+2 n -3,2 n -1] such that these integers are the cardinalities of row spaces R(A) of non-full rank Boolean matrices A of order n. We also show that for each s, where s=0,1,2,..., n-3, there exists A epsilon B n such that A is non-full rank and the cardinality of R(A) equals 2 n -2+2 n -3+2 s. 相似文献
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Zhou Bo 《Czechoslovak Mathematical Journal》2002,52(4):731-738
We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible. 相似文献
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Symplectic groups are well known as the groups of isometriesof a vector space with a non-singular bilinear alternating form.These notions can be extended by replacing the vector spaceby a module over a ring R, but if R is non-commutative, it willalso have to have an involution. We shall here be concernedwith symplectic groups over free associative algebras (witha suitably defined involution). It is known that the generallinear group GLn over the free algebra is generated by the setof all elementary and diagonal matrices (see [1, Proposition2.8.2, p. 124]). Our object here is to prove that the symplecticgroup over the free algebra is generated by the set of all elementarysymplectic matrices. For the lowest order this result was obtainedin [4]; the general case is rather more involved. It makes useof the notion of transduction (see [1, 2.4, p. 105]). When thereis only a single variable over a field, the free algebra reducesto the polynomial ring and the weak algorithm becomes the familiardivision algorithm. In that case the result has been provedin [3, Anhang 5]. 相似文献
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Zhong Lipin 《大学数学》1998,(3)
设Bn表示所有的n阶布尔矩阵的集合,R(A)表示A∈Bn的行空间,|R(A)|表示R(A)的基数.设m,n为正整数,本文证明了(Ⅰ)m∈[1,46],[1,78],分别存在A∈B7,A∈B8,使得|R(A)|=m.(Ⅱ)当n≥9为奇数时,则m∈[1,2(n+3)/2+2(n+1)/2+…+23],存在A∈Bn,使得|R(A)|=m. 相似文献
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在布尔运算下, 布尔矩阵A的幂敛指数和周期分别是使Ak=Ak+p成立的最小非负整数k和最小正整数p. 人们对周期的认识已经相当完善.给定满足一个不等式的正整数n和s, 利用组合分析确定了有向图含至少一个s -圈的n×n布尔矩阵的幂敛指数可以取得的数值. 相似文献
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本文重点讨论了布尔矩阵半群中的幂等、广义幂等、素矩阵以及它们之间的联系,对非负矩阵半群上的类零型结构也进行了研究. 相似文献
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The N-dimensional Roesser matrix is defined and shown to beessential to the formal solution of the N-dimensional Roesserequations. An extended Cayley-Hamilton theorem and a Leverrier-Fadeevtype algorithm are dervied for N-dminesional systems. One formof decomposition of the matrices is considered, and two particularcases are evaluated in terms of one-dimensional matrics. 相似文献