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1.
The inverses of conjugate-Toeplitz (CT) and conjugate-Hankel (CH) matrices can be expressed by the Gohberg–Heinig type formula. We obtain an explicit inverse formula of CT matrix. Similarly, the formula and the decomposition of the inverse of a CH matrix are provided. Also the stability of the inverse formulas of CT and CH matrices are discussed. Examples are provided to verify the feasibility of the algorithms.  相似文献   

2.
Constructing a kind of cyclic displacement, we obtain the inverse of conjugate-Toeplitz matrix by the aid of Gohberg-Semencul type formula. The stability of the inverse formula is discussed. Numerical examples are given to verify the feasibility of the inverse formula. We show how the analogue of our Gohberg-Semencul type formula leads to an efficient way to solve the conjugate-Toeplitz linear system of equations. It will be shown the number of real arithmetic operations is not more than known results. The corresponding conjugate-Hankel matrix is also considered.  相似文献   

3.
A complex matrix A = [aij] has been called conjugate-Toeplitz if aij = ci?1(ai?j), where c( ) denotes conjugation. A necessary and sufficient condition is derived for a matrix H to have a conjugate-Toeplitz inverse. The elements of H are generated from the coefficients of certain polynomials. The result is simplified either when H is to have a Toeplitz inverse, or when H is banded and is to have a conjugate-Toeplitz inverse. Each of these consequences of the main theorem is a different generalization of a previous result on banded matrices having a Toeplitz inverse.  相似文献   

4.
利用矩阵的奇异值分解讨论了一类广义双对称矩阵反问题,得到了此类矩阵反问题有解的充要条件及通解的表达式.  相似文献   

5.
先讨论两个可换对合阵P,Q线性组合aP+bQ可逆的充分必要条件及可逆时逆矩阵计算公式,再利用矩阵分解,以两种形式讨论两个可换对合阵P,Q组合aI+bP+cQ+dPQ及三个两两可换对合阵P,Q,R组合aI+bP+cQ+dPQ+eR+fPR+gQR+hPQR可逆的充分必要条件及可逆时分别给出逆矩阵计算公式.  相似文献   

6.
广义对称矩阵反问题有解的条件   总被引:2,自引:0,他引:2  
本利用矩阵的奇异值分解讨论了一类广义对矩阵阵反问题,得到了此类矩阵反问题有解的充分必要条件及通解的表达式。  相似文献   

7.
A square matrix A of order n is said to be tripotent if A 3?=?A. In this note, we give a nine-term disjoint idempotent decomposition for the linear combination of two commutative tripotent matrices and their products. Using the decomposition, we derive some closed-form formulae for the eigenvalues, determinant, rank, trace, power, inverse and group inverse of the linear combinations. In particular, we show that the linear combinations of two commutative tripotent elements and their products can produce 39?=?19,683 tripotent elements.  相似文献   

8.
左可正  谢涛 《数学杂志》2014,34(3):497-501
本文研究了当P与Q是两个复数域上的n阶幂等矩阵且满足PQP=PQ时,组合aP+bQ+cP Q+dQP+eQP Q的群逆问题,利用矩阵的分块及群逆的性质,证明了它是群逆阵,并且给出了其群逆的表达式,其中ab=0,a,b,c,d,e为复数.  相似文献   

9.
New necessary and sufficient conditions are given for a nonsingular matrix to have Hankel or Toeplitz form. Two generalizations, termed conjugate-Toeplitz and Leslie-Toeplitz matrices, are introduced A number of properties of Toeplitz matrices are shown to carry over to these extensions  相似文献   

10.
In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [12], Core EP inverse, Linear and Multilinear Algebra 62(3) (2014), 792–802. Firstly, we give a new representation and a new characterization of the core EP inverse. Then, we study some properties of the core EP inverse by using a representation by block matrices. Secondly, we extend the notion of core EP inverse to rectangular matrices by means of a weighted core EP decomposition. Finally, we study some properties of weighted core EP inverses.  相似文献   

11.
陈引兰  左可正  谢涛 《数学杂志》2015,35(5):1026-1034
本文研究了四个三幂等阵线性组合的可逆性及群逆.利用矩阵分解的方法,获得了它们可逆及群逆的一些条件,并得到其逆和群逆的计算公式,这些结论完善了k幂等阵可逆性理论.  相似文献   

12.
In this paper we present an analytical forms for the inversion of general periodic tridiagonal matrices, and provide some very simple analytical forms which immediately lead to closed formulae for some special cases such as symmetric or perturbed Toeplitz for both periodic and non-periodic tridiagonal matrices. An efficient computational algorithm for finding the inverse of any general periodic tridiagonal matrices from the analytical form is given, it is suited for implementation using Computer Algebra systems such as MAPLE, MATLAB, MACSYMA, and MATHEMATICA. An example is also given to illustrate the algorithm.  相似文献   

13.
In this paper,we extend the notion of the T-Schur decomposition to the weighted T-core-EP decomposition.Next,the weighted T-core-EP inverse of rectangular tensors is defined by a system,and its existence and uniqueness are obtained.Furthermore,the perturbation of the weighted T-core-EP inverse is studied under several conditions,and the relevant examples are provided to verify the perturbation bounds of the weighted T-core-EP inverse of tensors.  相似文献   

14.
非奇异矩阵的逆是矩阵元素的连续函数.学者们也对矩阵广义逆的连续性有所研究.本文应用矩阵分裂和两个矩阵之和的逆的展开式,给出了一般非奇异矩阵,M-矩阵和H-矩阵的逆的连续性.当一些合理的条件满足时,这几种矩阵的逆是连续的.  相似文献   

15.
In this paper we derive a general expression for integer powers of real upper and lower anti-bidiagonal matrices with constant anti-diagonals using Chebyshev polynomials. An explicit formula for the inverse of these matrices is also provided.  相似文献   

16.
It is shown how an algorithm for inverting Toeplitz matrices using O(n2) operations can be modified to deal with a certain type of extension, named conjugate-Toeplitz matrices. The block partitioned case is also included.  相似文献   

17.
In this paper, some new properties of the equality constrained and weighted least squares problem (WLSE) min W1/2(Kxg)2 subject to Lx=h are obtained. We derive a perturbation bound based on an unconstrained least squares problem and deduce some equivalent formulae for the projectors of this unconstrained LS problem. We also present a new way to compute the minimum norm solution xWLSE of the WLSE problem by using the QR decomposition of the corresponding matrices and propose an algorithm to compute xWLSE using the QR factorizations. Some numerical examples are provided to compare different methods for solving the WLSE problem.  相似文献   

18.
Hermite广义Hamilton矩阵反问题的最小二乘解   总被引:3,自引:0,他引:3  
钱爱林  柳学坤 《数学杂志》2006,26(5):519-523
本文研究了Hermite广义Hamilton矩阵反问题的最小二乘解,利用矩阵的奇异值分解,得到了解的表达式用Hermite广义Hamilton矩阵构造给定定矩阵的最佳逼近问题有解的条件.  相似文献   

19.
1.IntroductionThispaPerdealswiththeproblemofndniedingasumofsquaresofnonlinearfuntions-mwhereri(x),i==1,2,',maretwicecontinuouslyfferentiable,m2n'r(x)=(rl(x),rz(x),'jbe(x))"and"T"denotestranspose.NoIilinearleastSquaresproblemisakindofAnportan0ptiedationprobletnsandisaPpearedinmanyfield8suchasscientilicexperiments,mbomumlikelihoodestimation,solutionofnonlinearequaions'patternrecoghtionandetc.ThederiVativesofthefUnctionj(x)aregivenbywhereAEppxnistheJacobianmatrisofr(x)anditselementsare~=f…  相似文献   

20.
邓远北  文亚云 《计算数学》2018,40(3):241-253
针对线性代数方程组Ax=b,利用矩阵分解的思想,构造一类特殊五对角与七对角对称正定阵的矩阵分解,获得这类矩阵反问题解存在的充要条件和通解表达式.最后,给出了具体算法与数值算例.  相似文献   

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