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具有两个Jordan块的Jordan标准形的平方根矩阵 总被引:5,自引:0,他引:5
朱德高 《数学物理学报(A辑)》2000,20(4):451-460
J=Jm1,(λ1) Jm2 (λ2 )是具有两个 Jordan块的 Jordan标准形 ,则 J有平方根矩阵的充要条件是下列条件之一成立 :(i) λ1,λ2 均不为零 ;(ii) λ1,λ2 中有一个为零 ,不妨设 λ1=0 ,λ2 ≠ 0 ,则 m1=1 ;(iii) λ1=λ2 =0 ,且 m1=m2 或 m1 1 =m2 或 m2 1 =m1,并给出了 J之平方根矩阵的表达形式 . 相似文献
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设Z,N分别是全体整数和正整数的集合,Mm(Z)表示Z上m阶方阵的集合.本文运用Fermat大定理的结果证明了:对于取定的次数n∈N,n≥3,二阶矩阵方程Xn+Yn=λnI(λ∈Z,λ≠0,X,Y∈M2(Z),且X有一个特征值为有理数)只有平凡解;利用本原素因子的结果得到二阶矩阵方程Xn+Yn=(±1)nI(n∈N,n≥3,X,Y∈M2(Z))有非平凡解当且仅当n=4或gcd(n,6)=1且给出了全部非平凡解;通过构造整数矩阵的方法,证明了下面的矩阵方程有无穷多组非平凡解:■n∈N,Xn+Yn=λnI(λ∈Z,λ≠0,X,Y∈Mn(Z));X3+Y3=λ3I(λ∈Z,λ≠0,m∈N,m≥2,X,Y∈Mm(Z)). 相似文献
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读本刊文 [1 ]和文 [2 ]推出了几个椭圆和双曲线的姊妹圆的文章后 ,经过进一步研究发现一个有趣的问题 .现提出笔者的一个发现 ,供大家参考 .命题 平面上到两个定点的距离之比为定值λ(λ>0 ,λ≠ 1)的点的轨迹为圆 .证明 设两定点 A(m,0 ) ,B(- m,0 ) ,动点 P(x,y) .由已知得|PA||PB|=λ(λ≠ 1)或 |PB||PA|=λ(λ≠ 1) ,即 (x m) 2 y2(x - m) 2 y2 =λ或 (x - m) 2 y2(x m) 2 y2 =λ∴ (λ2 - 1) x2 ± 2 m(λ2 1) x (λ2 - 1) y2 =(1-λ2 ) m2 (λ≠ 1) (1)∴ (x± λ2 1λ2 - 1m) 2 y2 =4λ2 m2(λ… 相似文献
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标准Jacobi矩阵的混合型特征反问题 总被引:2,自引:0,他引:2
0 引言 本文讨论如下标准形式的Jacobi矩阵 其中a_i>0(i=1,2,…,n),b_i>0(i=1,2,…,n-1)。 对于Jacobi矩阵(对称三对角矩阵)的特征反问题,已有的成果[1],基本上集中在由两组频谱或两个特征对(指特征值及相应的特征向量)构造Jacobi矩阵的元素这样两类问题上,习惯上称之为频谱型或特征向量型反问题。本文提出且求解了第三类型——混合型特征反问题。即由一组频谱数据和一个特征向量构造矩阵元素的问题: 问题Ⅰ 给定正数λ~(1),λ~(2),…,λ~(n)和实向量x=(x_1,x_2,…,x_n)~T,其中x_1=1。构造一个标准形式的Jacobi矩阵J,使其第k阶顺序主子阵恰以λ~(k)(k=1,2,…,n)为其特征值。且(λ~(n),x)为其特征对。 问题Ⅱ 给定正数0<λ_1~(n)<λ_1~(n-1)<…<λ_1~(1)和正向量x=(x_1,x_2,…,x_n),其中x_=,x_k>0(k=2,…,n),构造一个标准形式的Jacobi矩阵J,使其第K阶顺序主子阵恰以λ_1~(k)为其最小特征值,而(λ~(n),x)为J的特征对。 问题Ⅲ 给定n个实数0<λ_1)<λ_2<…<λ_n和m个实数λ~(1),λ~(2),…,λ~(m)及m维向量x=(x_1,…,x_m)~T。构造n阶标准形式的Jaeobi矩阵J,使其第K阶顺序主子阵恰以λ~(k)(k=1,2,…,m)为其特征值,而(λ~(m),x)为第m阶顺序主子阵的特征对,且λ_k(k=1,2,…,n)为J的特征值。这里系大于或等 相似文献
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崔晋川 《数学的实践与认识》1984,(2)
<正> 在本文中,我们讨论问题(P) AX=B,X≥0的解的一些性质并证明有关的定理.其中 A 为 m×(m+1)实矩阵,B 为 m×n 实矩阵,A 和 B 的秩均为 m,矩阵 X≥0意指字典序非负.我们先引入下述定义.定义1.如果一个向量 a≠0且 a_j>0,这里 j=min{i|a_i≠0},即第一个非零分量是正的,就称 a 是字典序正的向量,写成 a>0.如果 a≠0且 a_j<0,这里 j=min{i|a_i≠0},就称 a 是字典序负的向量,写成 a<0.如果 a>0或 a=0,则称 a 是字典序非负向量,并且写成 a≥0.矩阵 H 如果它的每一个行向量都是字典序非负的,则 相似文献
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Kunyang Wang Feng Dai 《分析论及其应用》2007,23(1):50-63
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths. 相似文献
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ZHENG ShiJun 《分析论及其应用》2004,20(3)
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V. 相似文献
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《高校应用数学学报(英文版)》2014,29(4)
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with 相似文献
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《数学研究及应用》2014,(6)
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics. 相似文献
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A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6]. 相似文献
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Yuxian Zheng 《分析论及其应用》2006,22(2):136-140
In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p(R^n) into the Lebesgue space L^p with p 〈 1. 相似文献
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H. H. Cuenya M.D. Lorenzo C. N. Rodriguez 《分析论及其应用》2007,23(2):162-170
In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms. 相似文献
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