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1.
王卿文 《数学杂志》1996,16(2):157-162
设F和Ω分别表示一个对合反自同构的体,一个加强P除环,本文定义了Ω上的亚(半)正定矩阵,给出了矩阵方程AXA^*=B在F上有(斜)自共轭矩阵解及在Ω上有亚(半)正定矩阵解的充要条件及其解集的显式表示。  相似文献   

2.
利用标准形分别给出了复正定矩阵的合成矩阵为复正定矩阵和实正定矩阵的合成矩阵为实正定矩阵的充分必要条件,其结果简单而实用.  相似文献   

3.
关于亚正定矩阵的一个充分条件   总被引:4,自引:1,他引:3  
根据 Johnson给出的亚正定矩阵的定义 ,给出了一个关于亚正定矩阵的充分条件 .  相似文献   

4.
体上一矩阵方程组的次自共轭及斜亚半正定解   总被引:1,自引:0,他引:1  
姜学波 《数学季刊》2001,16(2):86-90
给出了体上的矩阵方程组[AmnXmn=AsnXnm=Osn]有次自共轭解和斜亚半正定解的充要条件及其通解表达式。  相似文献   

5.
复正定矩阵的充要条件   总被引:2,自引:0,他引:2  
本文研究Hermite正定矩阵、实正定矩阵的推广概念复正定矩阵,给出了复方阵复正定性的一些充分必要条件。  相似文献   

6.
两复正定矩阵之和必是复正定矩阵,但其积未必是复正定矩阵.研究了复矩阵之积的正定性,给出了复矩阵之积为复正定矩阵的一系列判定条件,获得了一些新的结果,改进并推广了K y Fan T aussky定理及Fe jer定理.  相似文献   

7.
广义正定矩阵的进一步研究   总被引:2,自引:1,他引:1  
基于正定矩阵的几个定义,首先给出了广义正定矩阵的一些新性质,其次研究了广义正定矩阵与H-矩阵、M-矩阵的关系,推广和改进了文献中的有关行列式不等式.  相似文献   

8.
研究正定矩阵的子矩阵,利用合同标准形分别给出了复正定矩阵的子式阵为复正定矩阵和实正定矩阵的子式阵为实正定矩阵的充分必要条件,其结果简单而实用.  相似文献   

9.
蒋忠樟 《数学年刊A辑》2006,27(2):239-246
文[2]证明了实对称正定矩阵的子式阵仍然是实对称正定矩阵,文[3]给出了一般的正定矩阵的的概念,本文利用标准型给出了一般正定矩阵的子式阵仍然是正定矩阵的充要条件.  相似文献   

10.
文[2]证明了实对称正定矩阵的子式阵仍然是实对称正定矩阵,文[3]给出了一般的正定矩阵的的概念,本文利用标准型给出了一般正定矩阵的子式阵仍然是正定矩阵的充要条件.  相似文献   

11.
An algorithm is developed which determines eigenvalues for a symmetric Toeplitz matrix. To this end, we substantiate the generality of eigenvalues problems for a symmetric Toeplitz matrix and for a persymmetric Hankel one. The latter is reduced to an eigenvalue problem for a persymmetric Jacobi matrix. In the even order case, the problem reduces to a Jacobi matrix with halved order.  相似文献   

12.
该文研究了反对称偏对称矩阵反问题的最小二乘解,得到了该问题解的表达式以及该问题有解的充分必要条件.证明了其最佳逼近解的存在性和唯一性,建立了其最佳逼近解的表达式,并给出了求最佳逼近解的数值算法和算例.  相似文献   

13.
Condition Numbers for Structured Least Squares Problems   总被引:2,自引:0,他引:2  
This paper studies the normwise perturbation theory for structured least squares problems. The structures under investigation are symmetric, persymmetric, skewsymmetric, Toeplitz and Hankel. We present the condition numbers for structured least squares. AMS subject classification (2000) 15A18, 65F20, 65F25, 65F50  相似文献   

14.
The problem of generating a matrix A with specified eigen‐pair, where A is a symmetric and anti‐persymmetric matrix, is presented. An existence theorem is given and proved. A general expression of such a matrix is provided. We denote the set of such matrices by ??????En. The optimal approximation problem associated with ??????En is discussed, that is: to find the nearest matrix to a given matrix A* by A∈??????En. The existence and uniqueness of the optimal approximation problem is proved and the expression is provided for this nearest matrix. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

15.
In this paper, we derive a general expression for the entries of the powers of any complex persymmetric or skew-persymmetric anti-tridiagonal matrix with constant anti-diagonals, in terms of the Chebyshev polynomials of the second kind.  相似文献   

16.
Suppose that p(XY) = A − BX − X(∗)B(∗) − CYC(∗) and q(XY) = A − BX + X(∗)B(∗) − CYC(∗) are quaternion matrix expressions, where A is persymmetric or perskew-symmetric. We in this paper derive the minimal rank formula of p(XY) with respect to pair of matrices X and Y = Y(∗), and the minimal rank formula of q(XY) with respect to pair of matrices X and Y = −Y(∗). As applications, we establish some necessary and sufficient conditions for the existence of the general (persymmetric or perskew-symmetric) solutions to some well-known linear quaternion matrix equations. The expressions are also given for the corresponding general solutions of the matrix equations when the solvability conditions are satisfied. At the same time, some useful consequences are also developed.  相似文献   

17.
Summary We present an exposé of the elementary theory of Jacobi matrices and, in particular, their reconstruction from the Gaussian weights and abscissas. Many recent works propose use of the diagonal Hermitian Lanczos process for this purpose. We show that this process is numerically unstable. We recall Rutishauser's elegant and stable algorithm of 1963, based on plane rotations, implement it efficiently, and discuss our numerical experience. We also apply Rutishauser's algorithm to reconstruct a persymmetric Jacobi matrix from its spectrum in an efficient and stable manner.Dedicated to Professor F.L. Bauer on the occasion of his 60th birthdayThis work was supported by the National Science Foundation under grant MCS-81-02344, and by the Mathematics Research Institute of the Swiss Federal Institute of Technology, Zürich  相似文献   

18.
The object of this paper is to develop some of the results in the author's joint paper with Dale [2] concerning the derivatives of persymmetric determinants whose elements are Appell functions.Four new double-sum identities are presented which are valid for arbitrary persymmetric determinants. Two of these identities are applied to give direct proofs of two results in [2], A simple formula is given for the derivative of a Turanian of order n with Appell polynomial elements and the result is applied repeatedly to show that its degree is far lower than expected. It is shown that one particular determinant has simple derivatives of all orders and that its degree too is far lower than expected. The formula for the derivative of (first) cofactors is shown to be extensible in a simple manner to the derivatives of second cofactors.  相似文献   

19.
A special class Tn of n×n matrices is described, which has tensor rank n over the real field. A tensor base for general symmetric, persymmetric, both symmetric and persymmetric matrices and Toeplitz symmetric matrices can be defined in terms of the tensor bases of Tl for some different values of l. It is proved that both symmetric and persymmetric n×n matrices and Toeplitz symmetric n×n matrices have tensor rank [(n+1)24] and 2n?2, respectively, in the real field.  相似文献   

20.
In this note it is shown that any square matrix AC n×n can be represented as the sum A= , where is complex symmetric and rank . The corresponding persymmetric result can be used in finding the terms of a small rank perturbed Toeplitz matrix via an O(n 2) computation. This allows one to perform fast matrix–vector products in case n is large.  相似文献   

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