共查询到18条相似文献,搜索用时 468 毫秒
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给出四种方法,分别根据特征多项式的性质,多项式根与系数之间的关系以及对称多项式的知识,k次本原单位根,特征多项式的伴侣阵,可在矩阵的特征多项式已知的情况下确定其矩阵方幂的特征多项式. 相似文献
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多项式判别矩阵的若干性质及其应用 总被引:3,自引:0,他引:3
具有文字系数的多项式f(x),其判别矩阵是f与f′的Sylvester矩阵通过添加一行一列而得,已经知道,判别矩阵的偶数阶主子式的符号确定了f(x)的相异根(实根、复根)的数目,这里介绍如何将奇数阶与偶数阶主子式相结合用以判定该多项式的相异负根或正根的数目,并进一步判定其在区间上的实根数,本文还研究了与判别矩阵相关的一些实用性质,并应用这些性质给出了4次键合多项式不能正分解的一组简洁的充分必要条件。 相似文献
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通过以λ为变量的多项式f(λ)定义了矩阵多项式f(A),并将矩阵多项式的计算方法推广到矩阵函数.同时给出了矩阵函数f(A)的又一种计算方法. 相似文献
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四元数矩阵理论中的几个概念间的关系 总被引:17,自引:0,他引:17
本文指出并改正文[1]中的错误,给出弱特征多项式[2]与重特征多项式[3]间的显式关系,同时也给出行列式[2]与重行列式[4]间的显式关系,最后讨论了左特征值、右特征值、特征值和特征根之间的关系及最小多项式与弱特征多项式根之间的关系. 相似文献
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数学通报一九八八年第九期发表了陈兴龙的“矩阵特征多项式的一种求法”一文,该文给出了求矩阵特征多项式的递椎方法,即 相似文献
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A new algorithm for computing all roots of polynomials with real coefficients is introduced. The principle behind the new algorithm is a fitting of the convolution of two subsequences onto a given polynomial coefficient sequence. This concept is used in the initial stage of the algorithm for a recursive slicing of a given polynomial into degree-2 subpolynomials from which initial root estimates are computed in closed form. This concept is further used in a post-fitting stage where the initial root estimates are refined to high numerical accuracy. A reduction of absolute root errors by a factor of 100 compared to the famous Companion matrix eigenvalue method based on the unsymmetric QR algorithm is not uncommon. Detailed computer experiments validate our claims. 相似文献
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系统地论证了二次自伴矩阵多项式特征值,特征向量的性质.给出了二次自伴矩阵多项式特征值与任一非零向量所对应的二次多项式根之间的大小关系;精确地给出了二次自伴矩阵多项式是负定时参数的界;简化了二次自伴矩阵多项式的符号特征是正(负)的特征值对应特征向量间可以是线性无关等定理的证明. 相似文献
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Mario Faliva 《Linear and Multilinear Algebra》2013,61(5):541-556
A solution to the problem of a closed-form representation for the inverse of a matrix polynomial about a unit root is provided by resorting to a Laurent expansion in matrix notation, whose principal-part coefficients turn out to depend on the non-null derivatives of the adjoint and the determinant of the matrix polynomial at the root. Some basic relationships between principal-part structure and rank properties of algebraic function of the matrix polynomial at the unit root as well as informative closed-form expressions for the leading coefficient matrices of the matrix-polynomial inverse are established. 相似文献
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This paper considers structured matrix methods for the calculation of the theoretically exact roots of a polynomial whose coefficients are corrupted by noise, and whose exact form contains multiple roots. The addition of noise to the exact coefficients causes the multiple roots of the exact form of the polynomial to break up into simple roots, but the algorithms presented in this paper preserve the multiplicities of the roots. In particular, even though the given polynomial is corrupted by noise, and all computations are performed on these inexact coefficients, the algorithms ‘sew’ together the simple roots that originate from the same multiple root, thereby preserving the multiplicities of the roots of the theoretically exact form of the polynomial. The algorithms described in this paper do not require that the noise level imposed on the coefficients be known, and all parameters are calculated from the given inexact coefficients. Examples that demonstrate the theory are presented. 相似文献
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We investigate the location of the eigenvalues of the Hermite matrix of a given complex polynomial, the question under what conditions a given polynomial and the characteristic polynomial of its Hermite matrix are identical, and the question under what conditions the Hermite matrix has only one distinct eigenvalue. 相似文献
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A Fibonacci–Hessenberg matrix with Fibonacci polynomial determinant is referred to as a polynomial Fibonacci–Hessenberg matrix. Several classes of polynomial Fibonacci–Hessenberg matrices are introduced. The notion of two-dimensional Fibonacci polynomial array is introduced and three classes of polynomial Fibonacci–Hessenberg matrices satisfying this property are given. 相似文献
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We investigated an interpolation algorithm for computing outer inverses of a given polynomial matrix, based on the Leverrier–Faddeev method. This algorithm is a continuation of the finite algorithm for computing generalized inverses of a given polynomial matrix, introduced in [11]. Also, a method for estimating the degrees of polynomial matrices arising from the Leverrier–Faddeev algorithm is given as the improvement of the interpolation algorithm. Based on similar idea, we introduced methods for computing rank and index of polynomial matrix. All algorithms are implemented in the symbolic programming language MATHEMATICA , and tested on several different classes of test examples. 相似文献
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The concept of a multiple root of matrix polynomial L(λ) is introduced, and associated spectral properties of L(λ) are investigated. A statement concerning factorization of L(λ) is presented. Applications are made to factorizations of the matrix polynomial Lα(λ), for any positive integer α. 相似文献