共查询到20条相似文献,搜索用时 218 毫秒
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本文研究了两个经典的Hermitian正定矩阵的Hadamard乘积的Bapat-Kwong矩阵不等式的推广,利用局部完全Hermitian矩阵的性质,根据可逆矩阵的主子矩阵与其Schur补的关系,得到了两个局部完全Hermitian矩阵的Hadamard乘积的矩阵不等式.所得到的结果不仅在放弃了正定性的前提下得到了经典的Bapat-Kwong矩阵不等式,而且还给出了这个矩阵不等式等式成立的充分必要条件. 相似文献
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范德蒙(Vandermonde)矩阵和柯西(Cauchy)矩阵是矩阵论中两个十分著名的矩阵,它们是判别几个矢量线性无关的十分有力的工具,因此在数学领域和其他工程技术中均有许多应用。本文推广了范德蒙矩阵和柯西矩阵,即定义一种广义范德蒙矩阵和广义柯西矩阵,它们在编码理论中具有十分重要的意义,本文介绍这两种矩阵的目的是期望它们将在数学领域和工程技术中得到更多的应用。记: 相似文献
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利用两个多项式的最大公因式的求法,给出了用辗转相除法求循环矩阵的逆矩阵的算法,该方法不需要计算循环矩阵的特征值。 相似文献
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循环矩阵与矩阵对角化 总被引:4,自引:0,他引:4
循环矩阵与矩阵对角化赵继安(甘肃省碌曲县中学747200)矩阵的相似关系具有反身性,对称性和传递性,所以相似关系也是一种等价关系.按相似关系将复数域C上的n阶矩阵分类,凡属同一个类的矩阵彼此相似,属于异类的任意两个矩阵都不相似,这样的类称为相似类.本... 相似文献
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本文研究两个迭代矩阵的渐近收敛率比较问题.基于K-非负矩阵理论,给出了关于两个K-弱分裂的比较定理,并指出这些结论是文献[Numer.Math.,2002,92(3):563-591]中相对应的结论的推广. 相似文献
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关于矩阵分解为对称矩阵的乘积 总被引:4,自引:0,他引:4
<正> 矩阵的乘积分解是矩阵论中有意义的问题之一,[3]中证明了任意域上的方阵都可表为不超过四个对称矩阵的乘积.本文将证明任意域上的方阵,都可表为两个对称矩阵的乘积.设 F 为一域,M_n(F)是 F 上所有 n×n 矩阵的集合,G_n(F)是 M_n(F)中非奇异矩阵所成的乘法群.设 S∈M_n(F),S~T 表示 S 的转置矩阵,如果 S=S~T,则称 S 为对称矩阵. 相似文献
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关于化矩阵为标准形时可逆矩阵求法的探讨 总被引:2,自引:0,他引:2
可逆矩阵在矩阵理论和应用中都起着十分重要的作用,本文就化矩阵为标准形时可逆矩阵的求法问题进行探讨,给出了利用矩阵的初等行、列变换同时求出两个可逆矩阵的一种简便实用的方法. 相似文献
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D. H. Lehmer 《Linear and Multilinear Algebra》1991,28(4):251-264
A matrix paraphrase of a certain body of facts dealing with real or complex numbers is a translation of these facts into matrix algebra in which the numbers are replaced by matrices. In two recent papers we developed matrix paraphrases of the Gaussian periods and the Klooster-mann sums. In this paper we paraphrase the theory of finite Fourier series and apply these results to Kloostermann matrices. 相似文献
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关于广义对角占优矩阵 总被引:7,自引:2,他引:5
若|a_(jj)|>σ_j,=1,…,n,则称A为(按行)严格对角占优矩阵。若为严格对角占优矩阵,则称A为共轭(严格)对角占优矩阵。关于各类对角占优矩阵特征值的分布,已在文献[1[[2]中作了研究,本文在此基础上对范围更广的两类矩阵的特征值分布取得一些结果,并且进一步分析了一类矩阵的一些性质。 相似文献
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Karla Rost 《Linear algebra and its applications》2012,436(10):3904-3918
Inverses of symmetric (or skewsymmetric) Toeplitz matrices as well as of centrosymmetric (or centro-skewsymmetric) Toeplitz-plus-Hankel matrices can be represented as sums of two split Bezoutians which are highly structured matrices since all of their rows and columns are symmetric or skewsymmetric vectors. Thus it is desirable to find matrix representations for split Bezoutians B. This is the main aim of the present paper.Recursion formulas for the entries of B are presented, bases of very simple split Bezoutians or of sparse matrices are constructed, and B is represented as a corresponding linear combination. Moreover, matrix representations of Gohberg/Semencul type are established. 相似文献
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Marko Huhtanen 《Arkiv f?r Matematik》2010,48(1):57-77
Nonsingular matrix subspaces can be separated into two categories: by being either invertible, or merely possessing invertible
elements. The former class was introduced for factoring matrices into the product of two matrices. With the latter, the problem
of characterizing the inverses and related nonlinear matrix geometries arises. For the singular elements there is a natural
concept of spectrum defined in terms of determinantal hypersurfaces, linking matrix analysis with algebraic geometry. With
this, matrix subspaces and the respective Grassmannians are split into equivalence classes. Conditioning of matrix subspaces
is addressed. 相似文献
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In this paper, we establish a group of closed-form formulas for the maximal and minimal ranks of a nonlinear matrix expression with respect to two variant matrices by using a linearization method and some known formulas for extremal ranks of linear matrix expressions. In addition, by using some pure algebraic operations of matrices and their generalized inverses, we derive the maximal and minimal ranks of the above nonlinear matrix expression, where the two variant matrices are any solutions of two consistent matrix equations. As an application, we derive some sufficient and necessary conditions for the existence of the solution of a nonlinear matrix function. 相似文献
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On the basis of the Euler identity, we obtain expansions for weighted pseudoinverse matrices with positive-definite weights in infinite matrix power products of two types: with positive and negative exponents. We obtain estimates for the closeness of weighted pseudoinverse matrices and matrices obtained on the basis of a fixed number of factors of matrix power products and terms of matrix power series. We compare the rates of convergence of expansions of weighted pseudoinverse matrices in matrix power series and matrix power products to weighted pseudoinverse matrices. We consider problems of construction and comparison of iterative processes of computation of weighted pseudoinverse matrices on the basis of the obtained expansions of these matrices.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1539–1556, November, 2004. 相似文献
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Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices. 相似文献
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证明了可选取矩阵X和Hermitian矩阵Z,使得下面的Hermitian型分块矩阵(A XX*Z)取得它的极大秩和极小秩,这里A*=A∈Cm×m是一个已知的复矩阵,X∈Cm×k和Z*=Z∈Ck×k是两个任意的复矩阵. 相似文献
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关于Toeplitz矩阵的某些注记 总被引:1,自引:0,他引:1
In this paper,we study real symmetric Toeplitz matrices commutable with tridi-agonal matrices, present more detailed results than those in [1], and extend them to non-symmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed. 相似文献