共查询到19条相似文献,搜索用时 62 毫秒
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黄炳家 《纯粹数学与应用数学》2002,18(3):267-271
文[1][2][3]中讨论AX=B的对称阵逆特征值问题,文[4][5][6]中讨论了半正定阵的逆特征值问题。本文讨论了空间了子空间上的对称正定及对称半正定阵的左右特征值反问题,给出了解存在的充分条件及解的表达式。 相似文献
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讨论n元实二次多项式f(x1,x2,…,xn)=(1 xT)A1x(x=(x1,…,xn)T)正定性的判定方法. 相似文献
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可读证明是不等式机器证明领域中的热点问题.针对具有对称零点的实轮换对称型,文章提出了其线性空间的一组基以及分拆算法和两种分拆形式用于对不等式进行可读证明研究.讨论了该线性空间的维数,以及轮换对称型半正定性的判别方法.给出了一类具有对称零点的轮换对称型的半正定性判定条件.大量实例表明此分拆方式在轮换对称型半正定性的判定及可读证明上具有很好的实用性. 相似文献
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对称部分为半正定的方阵 总被引:35,自引:0,他引:35
所有n阶具有半正定对称部分的方阵的集合记作PSDn.本文给出了PSDn中方阵在合同下的标准形以及PSDn中两个方阵合同的一个充要条件,并给出了PSDn中一个方阵及其对称部分与斜对称部分的主子式间的一个不等式. 相似文献
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线性流形上实对称半正定阵的一类反问题 总被引:3,自引:0,他引:3
袁永新 《高等学校计算数学学报》2000,22(2):153-158
1 引 言文中记Rn×m为所有n×m阶实阵集合,SRn×n为所有n阶实对称阵集合,Pn表示所有n阶实对称半正定阵集合,A≥0表示方阵A对称半正定.A+、R(A)、N(A)分别表示矩阵A的Moore-Penrose广义逆,列空间和零空间,‖·‖表示Froblnius范数.对于Z.Y∈Rn×k,令S={A∈Pn|AZ=Y,ZTY∈PK,R(YT)=R(YTZ)}(1.1) 现考虑如下问题:问题 给定X.B∈Rn×m,找A∈S,使得AX=B(1.2) 问题 给定A∈Rn×n,找A∈SE,使得‖A-A‖=infA∈SE‖A-A‖(1.3)其中SE是问题的解集合.问题与具有重要的应用背景,当Y=ZΛ,Λ=diag(λ1,λ2,… 相似文献
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线性流形上实对称半正定阵的一类逆特征值问题 总被引:17,自引:3,他引:14
线性流形上实对称半正定阵的一类逆特征值问题廖安平,郭忠(湖南大学应用数学系)ACLASSOFINVERSEEIGENVALUEPROBLEMSFORREALSYMMETRICSEMI-POSITIVEDEFINITEONALINEARMANIFOLD... 相似文献
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E.E. Allen 《Journal of Algebraic Combinatorics》1994,3(1):5-16
Let R(X) = Q[x
1, x
2, ..., x
n] be the ring of polynomials in the variables X = {x
1, x
2, ..., x
n} and R*(X) denote the quotient of R(X) by the ideal generated by the elementary symmetric functions. Given a S
n, we let g
In the late 1970s I. Gessel conjectured that these monomials, called the descent monomials, are a basis for R*(X). Actually, this result was known to Steinberg [10]. A. Garsia showed how it could be derived from the theory of Stanley-Reisner Rings [3]. Now let R(X, Y) denote the ring of polynomials in the variables X = {x
1, x
2, ..., x
n} and Y = {y
1, y
2, ..., y
n}. The diagonal action of S
n on polynomial P(X, Y) is defined as
Let R
(X, Y) be the subring of R(X, Y) which is invariant under the diagonal action. Let R
*(X, Y) denote the quotient of R
(X, Y) by the ideal generated by the elementary symmetric functions in X and the elementary symmetric functions in Y. Recently, A. Garsia in [4] and V. Reiner in [8] showed that a collection of polynomials closely related to the descent monomials are a basis for R
*(X, Y). In this paper, the author gives elementary proofs of both theorems by constructing algorithms that show how to expand elements of R*(X) and R
*(X, Y) in terms of their respective bases. 相似文献
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Γ是齐次对称康托集,对n个实数t_1,…,t_n讨论了交集Γ∩(Γ+t_1)∩…∩(Γ+t_n)≠(?)的条件,以及计算出Γ∩(Γ+t_1)∩…∩(Γ+t_n)的Hausdorff维数的精确表达式. 相似文献
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Aivars Lorencs 《Acta Appl Math》2007,97(1-3):69-78
The subject of the paper is the probability-theoretic properties of elementary symmetric polynomials σ
k
of arbitrary degree k in random variables X
i
(i=1,2,…,m) defined on special subsets of commutative rings ℛ
m
with identity of finite characteristic m. It is shown that the probability distributions of the random elements σ
k
(X
1,…,X
m
) tend to a limit when m→∞ if X
1,…,X
m
form a Markov chain of finite degree μ over a finite set of states V, V⊂ℛ
m
, with positive conditional probabilities. Moreover, if all the conditional probabilities exceed a prescribed positive number
α, the limit distributions do not depend on the choice of the chain.
相似文献
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Megan M. Kerr 《Annals of Global Analysis and Geometry》1997,15(5):437-445
In this paper we examine homogeneous Einstein–Weyl structures and classify them on compact irreducible symmetric spaces. We find that the invariant Einstein–Weyl equation is very restrictive: Einstein–Weyl structures occur only on those spaces for which the isotropy representation has a trivial component, for example, the total space of a circle bundle. 相似文献
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Evangelia Samiou 《Geometriae Dedicata》1997,65(2):161-165
A Riemannian manifold M is called 2-flat homogeneous if every geodesic is contained in some 2-flat , and if the group of isometries of M acts transitively on the set of pairs (p, ) with p . By a 2-flat we mean a closed, connected, flat, totally geodesic, 2-dimensional submanifold of M. It is proved in the paper that 2-flat homogeneous spaces are symmetric. 相似文献
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为了在并行和向量机上求解对称正定性方程且Ax=b,两组多分裂方法被考虑,中,把Galligain和Ruggiero的两级算术平均方法推广到两级多分裂方法并给出了一些合适的内分裂例子,同时讨论了所引起的两级多分裂方法的收敛性。 相似文献
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We factor the virtual Poincaré polynomial of every homogeneous space G/H, where G is a complex connected linear algebraic group and H is an algebraic subgroup, as t2u (t2–1)r QG/H(t2) for a polynomial QG/H with nonnegative integer coefficients. Moreover, we show that QG/H(t2) divides the virtual Poincaré polynomial of every regular embedding of G/H, if H is connected. 相似文献
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对带对称齐次核K(m,n)的级数算子T:T{an}=Σ_(n=1)~∞ K(m,n)an,{an}∈lω(n),l={{an)| an≥0,Σ_(n=1)~∞ω(n)an<+∞},本文研究了T的范数刻画,并讨论其应用. 相似文献
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关于对称性的一个定理及其应用 总被引:2,自引:0,他引:2
袁南桥 《数学的实践与认识》2007,37(21):203-208
在一个问题中存在某种对称性时,若能充分利用这一性质,常常可以起到化繁为简,变难为易的作用.本文给出一个关于对称性的定理,以及它在定积分中的一些应用.某些经典的定积分定理和一些已知的结论,均可作为其推论. 相似文献