共查询到18条相似文献,搜索用时 109 毫秒
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提出了任意域上鳞状循环因子矩阵 ,利用多项式环的理想的Go bner基的算法给出了任意域上鳞状循环因子矩阵的极小多项式和公共极小多项式的一种算法 .同时给出了这类矩阵逆矩阵的一种求法 .在有理数域或模素数剩余类域上 ,这一算法可由代数系统软件Co CoA4 .0实现 .数值例子说明了算法的有效性 相似文献
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本文利用多项式的最大公因式给出的求r-循环矩阵和对称r-循环矩阵求逆的快速算法。该方法不需要计算三角函数并且具有很少的计算量。 相似文献
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本文利用多项式最大公因式 ,给出了线性方程组的反问题在 r-循环矩阵类和对称 r-循环矩阵类中有唯一解的充要条件 ,进而得到线性方程组在 r循环矩阵类和对称 r-循环矩阵类中的反问题求唯一解的算法 .最后给出了应用该算法的数值例子 . 相似文献
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详细地研究了有限域Fq上的矩阵的阶的问题,得到了相当理想的结果。并给出一类矩阵方幂的极小多项式的求法。 相似文献
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师白娟 《纯粹数学与应用数学》2016,32(3):305-317
行首加r尾r右循环矩阵和行尾加r首r左循环矩阵是两种特殊类型的矩阵,这篇论文中就是利用多项式因式分解的逆变换这一重要的技巧以及这类循环矩阵漂亮的结构和切比雪夫多项式的特殊的结构,分别讨论了第一类、第二类切比雪夫多项式的关于行首加r尾r右循环矩阵和行尾加r首r左循环矩阵的行列式,从而给出了行首加r尾r右循环矩阵和行尾加r首r左循环矩阵的行列式显式表达式.这些显式表达式与切比雪夫多项式以及参数r有关.这一问题的应用背景主要在循环编码,图像处理等信息理论方面. 相似文献
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利用多项式因式分解的逆变换,结合循环矩阵和切比雪夫多项式的特殊结构,首先研究第三类和第四类切比雪夫多项式的通项公式,并给出第三类、第四类切比雪夫多项式的关于行首加r尾r右循环矩阵和行尾加r首r左循环矩阵的行列式的显式表达式,最后给出算法实施步骤. 相似文献
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详细地研究了有限域 Fq上的矩阵的阶的问题 ,得到了相当理想的结果 .并给出一类矩阵方幂的极小多项式的求法 相似文献
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r-循环线性系统求解的快速算法 总被引:6,自引:0,他引:6
本文给出r-循环线性系统求解的一种快速算法.当r-循环矩阵非奇异时,该快速算法求出该线性系统的唯一解;当r-循环矩阵奇异时,该快速算法求出该线性系统的通解. 相似文献
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In this paper, algorithms for computing the minimal polynomial and the common minimal polynomial of resultant matrices over any field are presented by means of the approach for the Gröbner basis of the ideal in the polynomial ring, respectively, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with resultant blocks over any field is given, which can be realized by CoCoA 4.0, an algebraic system over the field of rational numbers or the field of residue classes of modulo prime number. We get examples showing the effectiveness of the algorithms. 相似文献
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Amir Hashemi Benyamin M.-Alizadeh Mahdi Dehghani Darmian 《Linear and Multilinear Algebra》2013,61(2):265-272
In this article, we study the minimal polynomials of parametric matrices. Using the concept of (comprehensive) Gröbner systems for parametric ideals, we introduce the notion of a minimal polynomial system for a parametric matrix, i.e. we decompose the space of parameters into a finite set of cells and for each cell we give the corresponding minimal polynomial of the matrix. We also present an algorithm for computing a minimal polynomial system for a given parametric matrix. 相似文献
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In this work, free multivariate skew polynomial rings are considered, together with their quotients over ideals of skew polynomials that vanish at every point (which includes minimal multivariate skew polynomial rings). We provide a full classification of such multivariate skew polynomial rings (free or not) over finite fields. To that end, we first show that all ring morphisms from the field to the ring of square matrices are diagonalizable, and that the corresponding derivations are all inner derivations. Secondly, we show that all such multivariate skew polynomial rings over finite fields are isomorphic as algebras to a multivariate skew polynomial ring whose ring morphism from the field to the ring of square matrices is diagonal, and whose derivation is the zero derivation. Furthermore, we prove that two such representations only differ in a permutation on the field automorphisms appearing in the corresponding diagonal. The algebra isomorphisms are given by affine transformations of variables and preserve evaluations and degrees. In addition, ours proofs show that the simplified form of multivariate skew polynomial rings can be found computationally and explicitly. 相似文献
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We define alternant codes over a commutative ring R and a corresponding key equation. We show that when the ring is a domain, e.g. the p-adic integers, the error-locator polynomial is the unique monic minimal polynomial (equivalently, the unique shortest linear recurrence) of the finite sequence of syndromes and that it can be obtained by Algorithm MR of Norton.WhenR is a local ring, we show that the syndrome sequence may have more than one (monic) minimal polynomial, but that all the minimal polynomials coincide modulo the maximal ideal ofR . We characterise the set of minimal polynomials when R is a Hensel ring. We also apply these results to decoding alternant codes over a local ring R: it is enough to find any monic minimal polynomial over R and to find its roots in the residue field. This gives a decoding algorithm for alternant codes over a finite chain ring, which generalizes and improves a method of Interlando et. al. for BCH and Reed-Solomon codes over a Galois ring. 相似文献
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Modified block preconditioner for generalized saddle point matrices with highly singular(1,1) blocks
《Linear and Multilinear Algebra》2012,60(1):152-160
ABSTRACTIn this paper, based on the preconditioners presented by Zhang [A new preconditioner for generalized saddle matrices with highly singular(1,1) blocks. Int J Comput Maths. 2014;91(9):2091-2101], we consider a modified block preconditioner for generalized saddle point matrices whose coefficient matrices have singular (1,1) blocks. Moreover, theoretical analysis gives the eigenvalue distribution, forms of the eigenvectors and the minimal polynomial. Finally, numerical examples show the eigenvalue distribution with the presented preconditioner and confirm our analysis. 相似文献
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This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was only achieved by resorting to genericity assumptions or randomization techniques, while the best known complexity bound with a general deterministic algorithm was obtained by Keller-Gehrig in 1985 and involves logarithmic factors. Our algorithm computes more generally the determinant of a univariate polynomial matrix in reduced form, and relies on new subroutines for transforming shifted reduced matrices into shifted weak Popov matrices, and shifted weak Popov matrices into shifted Popov matrices. 相似文献
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广义四元数体上矩阵的最小多项式 总被引:15,自引:3,他引:15
本文给出了广义四元数体上方阵的最小多项式与最小中心多项式的构造公式,讨论了它们的性质及其应用,得到广义四元数方阵相似于对角矩阵的一个充要条件。 相似文献
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本文研究了对称阵的最小多项式的存在唯一性,利用对称阵的正交分解的基本思想,获得了对称阵的最小多项式的具体表示形式,改进了Hamilton-Caylay定理.并且给出了对称阵最小多项式的几个应用. 相似文献