共查询到20条相似文献,搜索用时 15 毫秒
1.
V.M. Sidelnikov 《Journal of Algebraic Combinatorics》1999,10(3):279-288
We consider a finite subgroup
n
of the group O(N) of orthogonal matrices, where N = 2
n
, n = 1, 2 .... This group was defined in [7]. We use it in this paper to construct spherical designs in 2
n
-dimensional Euclidean space R
N
. We prove that representations of the group
n
on spaces of harmonic polynomials of degrees 1, 2 and 3 are irreducible. This and the earlier results [1–3] imply that the orbit
n,2
x
t
of any initial point x on the sphere S
N – 1 is a 7-design in the Euclidean space of dimension 2
n
. 相似文献
2.
矩阵Frobenius范数不等式 总被引:1,自引:0,他引:1
1 引言与引理 矩阵范数与矩阵奇异值问题是数值代数的重要课题,并在矩阵扰动分析,数值计算等分支中起着重要作用.国内外学者对此已作了大量研究. 相似文献
3.
Commutator inequalities associated with the polar decomposition 总被引:1,自引:0,他引:1
Fuad Kittaneh 《Proceedings of the American Mathematical Society》2002,130(5):1279-1283
Let be a polar decomposition of an complex matrix . Then for every unitarily invariant norm , it is shown that
where denotes the operator norm. This is a quantitative version of the well-known result that is normal if and only if . Related inequalities involving self-commutators are also obtained.
where denotes the operator norm. This is a quantitative version of the well-known result that is normal if and only if . Related inequalities involving self-commutators are also obtained.
4.
用Mn表示所有复矩阵组成的集合.对于A∈Mn,σ(A)=(σ1(A),…,σn(A)),其中σ1(A)≥…≥σn(A)是矩阵A的奇异值.本文给出证明:对于任意实数α,A,B∈Mn为半正定矩阵,优化不等式σ(A-|α|B) wlogσ(A+αB)成立,改进和推广了文[5]的结果. 相似文献
5.
Ning Wei 《Optimization》2016,65(10):1791-1803
6.
线性流形上对称正交反对称矩阵反问题的最小二乘解 总被引:1,自引:0,他引:1
设P是n阶对称正交矩阵,如果n阶矩阵A满足AT=A和(PA)T=-PA,则称A为对称正交反对称矩阵,所有n阶对称正交反对称矩阵的全体记为SARnp.令S={A∈SARnp f(A)=‖AX-B‖=m in,X,B〗∈Rn×m本文讨论了下面两个问题问题Ⅰ给定C∈Rn×p,D∈Rp×p,求A∈S使得CTAC=D问题Ⅱ已知A~∈Rn×n,求A∧∈SE使得‖A~-A∧‖=m inA∈SE‖A~-A‖其中SE是问题Ⅰ的解集合.文中给出了问题Ⅰ有解的充要条件及其通解表达式.进而,指出了集合SE非空时,问题Ⅱ存在唯一解,并给出了解的表达式,从而得到了求解A∧的数值算法. 相似文献
7.
8.
This paper investigates some properties of Euclidean distance matrices (EDMs) with focus on their ordering structure. The ordering treated here is the group majorization ordering induced by the group of permutation matrices. By using this notion, we establish two monotonicity results for EDMs: (i) The radius of a spherical Euclidean distance matrix (spherical EDM) is increasing with respect to the group majorization ordering. (ii) The larger an EDM is in terms of the group majorization ordering, the more spread out its eigenvalues are. Minimal elements with respect to this ordering are also described. 相似文献
9.
YANGHU 《高校应用数学学报(英文版)》1995,10(2):133-140
In this paper we discuss the generalizations of the Kantorovich inequality and obtain some generalized Kantorovich inequalities in the sense of matrix norm. We further illustrate how to use these inequalities to determine the lower bound of relative efficiency of the parameter estimate in linear model. 相似文献
10.
A. S. Gorsky 《Theoretical and Mathematical Physics》2007,150(2):175-186
We investigate the anomalous dimensions of (super)conformal Wilson operators in the weak-and strong-coupling regimes using
the integrability symmetry on both sides of the gauge/string correspondence. We study the origin of the single-logarithmic
asymptotic behavior of long operators/strings in the limit of large Lorentz spin.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 204–218, February, 2007. 相似文献
11.
M. Cera J. A. Mesa F. A. Ortega F. Plastria 《Journal of Optimization Theory and Applications》2008,136(2):155-166
Protection, surveillance or other types of coverage services of mobile points call for different, asymmetric distance measures
than the traditional Euclidean, rectangular or other norms used for fixed points. In this paper, the destinations are mobile
points (prey) moving at fixed speeds and directions and the facility (hunter) can capture them using one of two possible strategies:
either it is smart, predicting the prey’s movement in order to minimize the time needed to capture it, or it is dumb, following
a pursuit curve, by moving at any moment in the direction of the prey. In either case, the hunter location in a plane is sought
in order to minimize the maximum time of capture of any prey. An efficient solution algorithm is developed that uses the particular
geometry that both versions of this problem possess. In the case of unpredictable movement of prey, a worst-case type solution
is proposed, which reduces to the well-known weighted Euclidean minimax location problem.
The work of the second and third authors was supported in part by a grant from Research Projects BFM2003-04062 and MTM2006-15054. 相似文献
12.
A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let and be two Hermitian matrices, and let and be their eigenvalues arranged in ascending order. Then for any unitarily invariant norm . In this paper, we generalize this to the perturbation theory for diagonalizable matrix pencils with real spectra. The much studied case of definite pencils is included in this.
13.
Ren-Cang Li. 《Mathematics of Computation》2003,72(242):715-728
This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.
14.
Let r 1, …, r m be positive real numbers and A 1, …, A m be n × n matrices with complex entries. In this article, we present a necessary and sufficient condition for the existence of a unitarily invariant norm ‖·‖, such that ‖A i ‖ = r i , for i = 1, …, m. Then we identify the greatest unitarily invariant norm which satisfies this condition. Using this, we get an approximation of unitarily invariant norms. Although the minimum unitarily invariant norm which satisfies this condition does not exist in general, we find conditions over A i s and r i s which are sufficient for the existence of such a norm. Finally, we get a characterization of unitarily invariant norms. 相似文献
15.
E. K. Leinartas 《Siberian Mathematical Journal》1989,30(2):250-255
Lesosibirsk, Krasnoyarsk District. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 2, pp. 102–107, March–April, 1989. 相似文献
16.
Let ‖·‖ be a norm on the algebra ?n of all n × n matrices over ?. An interesting problem in matrix theory is that “Are there two norms ‖·‖1 and ‖·‖2 on ?n such that ‖A‖ = max|‖Ax‖2: ‖x‖1 = 1} for all A ∈ ?n?” We will investigate this problem and its various aspects and will discuss some conditions under which ‖·‖1 = ‖·‖2. 相似文献
17.
B. P. Duggal 《Proceedings of the American Mathematical Society》1998,126(7):2047-2052
Given a Hilbert space , let be operators on . Anderson has proved that if is normal and , then for all operators . Using this inequality, Du Hong-Ke has recently shown that if (instead) , then for all operators . In this note we improve the Du Hong-Ke inequality to for all operators . Indeed, we prove the equivalence of Du Hong-Ke and Anderson inequalities, and show that the Du Hong-Ke inequality holds for unitarily invariant norms.
18.
19.
Improved Young and Heinz inequalities for matrices 总被引:2,自引:0,他引:2
Fuad Kittaneh Yousef Manasrah 《Journal of Mathematical Analysis and Applications》2010,361(1):262-269
We give refinements of the classical Young inequality for positive real numbers and we use these refinements to establish improved Young and Heinz inequalities for matrices. 相似文献
20.
Tin-Yau Tam 《Proceedings of the American Mathematical Society》1999,127(1):35-44
For any , let be the following subset of :
We show that if , then is always convex. When , it is an ellipsoid, probably degenerate. The convexity result is best possible in the sense that if we have defined similarly, then there are examples which fail to be convex when and .
The set is also symmetric about the origin for all , and contains the origin when . Equivalent statements of this result are given. The convexity result for is similar to Au-Yeung and Tsing's extension of Westwick's convexity result for .