共查询到18条相似文献,搜索用时 46 毫秒
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本文利用矩阵运算、矩阵相似关系及矩阵的秩,深化了Jordan矩阵的性质,并在此基础上刻画了矩阵Jordan标准形中Jordan块的个数及阶数,最后讨论了矩阵多项式Jordan标准形,充实了高等代数中Jordan标准形的结果. 相似文献
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余览娒 《应用数学与计算数学学报》2002,16(2):61-67
本文利用一般域上的λ-矩阵理论,研究了矩阵多项式方程的可解性,证明了完全域上矩阵多项式方程有解的充要条件,这些条件同时提供了解此类矩阵方程的方法。 相似文献
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Mike Develin 《Order》2006,23(2-3):179-195
A natural construction due to K. Ding yields Schubert varieties from Ferrers boards. The poset structure of the Schubert cells in these varieties is equal to the poset of maximal rook placements on the Ferrers board under the Bruhat order. We determine when two Ferrers boards have isomorphic rook posets. Equivalently, we give an exact categorization of when two Ding Schubert varieties have identical Schubert cell structures. This also produces a complete classification of isomorphism types of lower intervals of 312-avoiding permutations in the Bruhat order. 相似文献
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给定数域F上的方阵A,借助等价标准形和数学归纳法证明了如果存在数域F上互素的一次因式乘积的多项式是A的零化多项式,则A可对角化. 相似文献
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《代数通讯》2013,41(5):2015-2017
Abstract We show that every element of the integral closure D′ of a domain D occurs as a coefficient of the minimal polynomial of a matrix with entries in D. This answers affirmatively a question of Brewer and Richman, namely, if integrally closed domains are characterized by the property that the minimal polynomial of every square matrix with entries in D is in D[x]. It follows that a domain D is integrally closed if and only if for every matrix A with entries in D the null ideal of A, N D (A)?=?{f?∈?D[x]?∣?f(A)?=?0} is a principal ideal of D[x]. 相似文献
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Nicolau C. Saldanha 《Journal of Algebraic Combinatorics》2002,16(2):195-207
Kasteleyn counted the number of domino tilings of a rectangle by considering a mutation of the adjacency matrix: a Kasteleyn matrix K. In this paper we present a generalization of Kasteleyn matrices and a combinatorial interpretation for the coefficients of the characteristic polynomial of KK* (which we call the singular polynomial), where K is a generalized Kasteleyn matrix for a planar bipartite graph. We also present a q-version of these ideas and a few results concerning tilings of special regions such as rectangles. 相似文献
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Skew Hadamard difference sets have been an interesting topic of study for over 70 years. For a long time, it had been conjectured the classical Paley difference sets (the set of nonzero quadratic residues in where ) were the only example in Abelian groups. In 2006, the first author and Yuan disproved this conjecture by showing that the image set of is a new skew Hadamard difference set in with m odd, where denotes the first kind of Dickson polynomials of order n and . The key observation in the proof is that is a planar function from to for m odd. Since then a few families of new skew Hadamard difference sets have been discovered. In this paper, we prove that for all , the set is a skew Hadamard difference set in , where m is odd and . The proof is more complicated and different than that of Ding‐Yuan skew Hadamard difference sets since is not planar in . Furthermore, we show that such skew Hadamard difference sets are inequivalent to all existing ones for by comparing the triple intersection numbers. 相似文献
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The zero set of one general multivariate polynomial is enclosed by unions and intersections of funnel-shaped unbounded sets. There are sharper enclosures for the zero set of a polynomial in two complex variables with complex interval coefficients. Common zeros of a polynomial system can be located by an appropriate intersection of these enclosure sets in an appropriate space. The resulting domain is directly brought into polynomial equation solvers. 相似文献
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James Haglund 《Advances in Applied Mathematics》1998,20(4):450-487
Connections betweenq-rook polynomials and matrices over finite fields are exploited to derive a new statistic for Garsia and Remmel'sq-hit polynomial. Both this new statisticmatand another statistic for theq-hit polynomial ξ recently introduced by Dworkin are shown to induce different multiset Mahonian permutation statistics for any Ferrers board. In addition, for the triangular boards they are shown to generate different families of Euler–Mahonian statistics. For these boards the ξ family includes Denert's statisticden, and gives a new proof of Foata and Zeilberger's Theorem that (exc, den) is equidistributed with (des, maj). Thematfamily appears to be new. A proof is also given that theq-hit polynomials are symmetric and unimodal. 相似文献