共查询到19条相似文献,搜索用时 44 毫秒
1.
对称正交对称矩阵逆特征值问题 总被引:27,自引:0,他引:27
Let P∈ Rn×n such that PT = P, P-1 = PT.A∈Rn×n is termed symmetric orthogonal symmetric matrix ifAT = A, (PA)T = PA.We denote the set of all n × n symmetric orthogonal symmetric matrices byThis paper discuss the following two problems:Problem I. Given X ∈ Rn×m, A = diag(λ1,λ 2, ... ,λ m). Find A SRnxnP such thatAX =XAProblem II. Given A ∈ Rnδn. Find A SE such thatwhere SE is the solution set of Problem I, ||·|| is the Frobenius norm. In this paper, the sufficient and necessary conditions under which SE is nonempty are obtained. The general form of SE has been given. The expression of the solution A* of Problem II is presented. We have proved that some results of Reference [3] are the special cases of this paper. 相似文献
2.
THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE 总被引:2,自引:0,他引:2
Zhen-yun Peng 《计算数学(英文版)》2003,21(4):505-512
In this paper, the following two problems are considered:Problem Ⅰ. Given S∈E Rn×p,X,B 6 Rn×m, find A ∈ SRs,n such that AX = B, where SR8,n = {A∈ Rn×n|xT(A - AT) = 0, for all x ∈ R(S)}.Problem Ⅱ. Given A* ∈ Rn×n, find A ∈ SE such that ||A-A*|| = minA∈sE||A-A*||, where SE is the solution set of Problem Ⅰ.The necessary and sufficient conditions for the solvability of and the general form of the solutions of problem Ⅰ are given. For problem Ⅱ, the expression for the solution, a numerical algorithm and a numerical example are provided. 相似文献
3.
Dongxiu Xie+ 《计算数学(英文版)》2003,21(2):167-174
This paper is mainly concerned with solving the following two problems: Problem Ⅰ. Given X ∈ Rn×m, B . Rm×m. Find A ∈ Pn such thatwhereProblem Ⅱ. Given A ∈Rn×n. Find A ∈ SE such thatwhere F is Frobenius norm, and SE denotes the solution set of Problem I.The general solution of Problem I has been given. It is proved that there exists a unique solution for Problem II. The expression of this solution for corresponding Problem II for some special case will be derived. 相似文献
4.
褚玉明 《数学物理学报(B辑英文版)》2005,25(3):492-504
The main aim of this paper is to discuss the following two problems:λm)∈Hm×m, find A ∈ BSH≥n×n such that AX= X∧, where BSH≥n×n denotes the set of all n × n quaternion matrices which are bi-self-conjugate and nonnegative definite.Problem Ⅱ:Given B ∈ Hn×m, find -B∈SE such that ||B- B||Q = minA∈sE ||B - A||Q,necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given. 相似文献
5.
THE SOLVABILITY CONDITIONS FOR INVERSE EIGENVALUE PROBLEM OF ANTI-BISYMMETRIC MATRICES 总被引:3,自引:0,他引:3
Dong-xiu Xie 《计算数学(英文版)》2002,(3)
AbstractThis paper is mainly concerned with solving the following two problems: Problem I. Given X Cnxm, A = diag( 1, 2, ..... , m) Cmxm . Find A ABSRnxn such thatAX = XAwhere ABSRnxn is the set of all real n x n anti-bisymmetric matrices. Problem II. Given A RnXn. Find A SE such thatwhere || || is Frobenius norm, and SE denotes the solution set of Problem I.The necessary and sufficient conditions for the solvability of Problem I have been studied. The general form of SB has been given. For Problem II the expression of the solution has been provided. 相似文献
6.
Xiaoping Pan Xiyan Hu Lei Zhang College of Mathematics Econometrics Hunan University Changsha China. 《高等学校计算数学学报(英文版)》2006,15(3):227-236
Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper discusses the following two problems. The first one is as follows. Given Z∈Rn×m (m < n),∧= diag(λ1,...,λm)∈Rm×m, andα,β∈R withα<β. Find a subset (?)(Z,∧,α,β) of SRrn×n(S) such that AZ = Z∧holds for any A∈(?)(Z,∧,α,β) and the remaining eigenvaluesλm 1 ,...,λn of A are located in the interval [α,β], Moreover, for a given B∈Rn×n, the second problem is to find AB∈(?)(Z,∧,α,β) such that where ||.|| is the Frobenius norm. Using the properties of symmetric reflexive matrices, the two problems are essentially decomposed into the same kind of subproblems for two real symmetric matrices with smaller dimensions, and then the expressions of the general solution for the two problems are derived. 相似文献
7.
This paper discusses problem IEP:Given n×m matrix X and m×m diagonal matrix A, find an n×n matrix A such that AX=XA.The new solvablily conditions for the problem IEP are obtained. The eigenvalue dislribulaion of the solutions for the problem IEP are described in detail. 相似文献
8.
Let A and C denote real n × n matrices. Given real n-vectors x1, ... ,xm, m ≤ n, and a set of numbers L = {λ1,λ2,... ,λm}. We describe (I) the set (?) of all real n × n bisymmetric positive seidefinite matrices A such that Axi is the "best" approximate to λixi, i = 1,2,...,m in Frobenius norm and (II) the Y in set (?) which minimize Frobenius norm of ||C - Y||.An existence theorem of the solutions for Problem I and Problem II is given and the general expression of solutions for Problem I is derived. Some sufficient conditions under which Problem I and Problem II have an explicit solution is provided. A numerical algorithm of the solution for Problem II has been presented. 相似文献
9.
《高等学校计算数学学报(英文版)》2000,(Z1)
1 IntroductionLet R~(n×n) be the set of all n×n real matrices.R~n=R~(n×1).C~(n×n)denotes the set of all n×n complex matrices.We are interested in solving the following inverse eigenvalue prob-lems:Problem A (Additive inverse eigenvalue problem) Given an n×n real matrix A=(a_(ij)),and n distinct real numbers λ_1,λ_2,…,λ_n,find a real n×n diagonal matrix D=diag 相似文献
10.
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
11.
12.
FANG FUQUAN 《数学年刊B辑(英文版)》2000,(4)
1. IntroductionBy [111, a hypersurface in a symmetric space is called equifocal if every normal geodesicperpendiculajr to it is closed of constant length, say l, and contains Zg focal points for somepositive integer g. This is a natural generalization of isoparametric hypersurfaces in sphereswhere the illteger g is the number of distinct principal curvatures. In this note we considerequifocal hypersurfaces in simply connected rank one symmetric spaces, i.e. the complexprojective space CP", th… 相似文献
13.
14.
Let Sn be the symmetric group,g+I=(123i),g-I=(1i32) and M+n={g+I:4≤I≤n},then M+n is a minimal generating set of Sn,where n≥5.It is proved that Cayley graph Cay(Sn,M+n∪M-n) is Hamiltonian and edge symmetric. 相似文献
15.
TONG Jingcheng 《数学年刊B辑(英文版)》2004,25(1):139-142
§1. Introduction Let ξbe an irrational number with simple continued fraction expansion ξ= [a0;a1,···,ai,···]and pi be its ith convergent. In [1], the present author considered the well-known inequality q 相似文献
16.
ON SYMMETRIC SCALAR CURVATURE ON 总被引:1,自引:0,他引:1
JI Min 《数学年刊B辑(英文版)》1999,20(3):325-330
1.IntroductionGivenacontinuousfunctionRonthestandardsphereS',itisaninterestingproblemwhetherRcanbethescalarcurvatureofsomemetricgwhichispointwiseconformaltothestandardmetricgoonS2.Ifwesetg~e"go,whereuisafunctiononS',theproblemisequivalenttothesolvabilityofthefollowingPDE:--A..u 2--Re"=0,onS2.(l'1)KazdanandWarner[9]pointedoutthatitmaybeinsolvable.Inthelastfewyears,alotofworkhasbeendonetosolveproblem(l.l),especiallywhenRpossessessomekindsofsymmetries.AfterthepioneerworkduetoMoser[lo]forthe… 相似文献
17.
We give a complete classification of the reductive symmetric pairs (G, H) for which the homogeneous space (G × H)/ diag H is real spherical in the sense that a minimal parabolic subgroup has an open orbit. Combining with a criterion established in T. Kobayashi, T. Oshima, Adv. Math. 2013, we give a necessary and sufficient condition for a reductive symmetric pair (G, H) such that the multiplicities for the branching law of the restriction of any admissible smooth representation of G to H have finiteness/boundedness property. 相似文献
18.
FANG Fuquan 《数学年刊B辑(英文版)》2000,21(4):473-478
This note investigates the multiplicity problem of principal curvatures of equifocal hypersurfaces in simply connected rank
1 symmetric spaces. Using Clifford representation theory, and the author also constructs infinitely many equifocal hypersurfaces
in the symmetric spaces.
Project supported by the National Natural Science Foundation of China (No. 19925104), RFDP and the Qiu-Shi Science and Technology
Foundation. 相似文献
19.
Ying Jianggang 《数学年刊B辑(英文版)》1998,19(1):81-86
STRONGSUBORDINATIONOFSYMMETRICDIRICHLETFORMSYINGJIANGGANGManuscriptreceivedMay9,1995.RevisedMarch21,1996.DepartmentofMath... 相似文献