Equivalence Representation for Nonsingular M-matrices

ＥｑｕｉｖａｌｅｎｃｅＲｅｐｒｅｓｅｎｔａｔｉｏｎｆｏｒＮｏｎｓｉｎｇｕｌａｒＭ－ｍａｔｒｉｃｅｓＳｕｎＹｕｘｉａｎｇ（孙玉祥）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅＪｉｌｉｎ，１３２０１１）Ａｂ...     

Equivalent Representations of Complex Positive Definite Matrices

ＥｑｕｉｖａｌｅｎｔＲｅｐｒｅｓｅｎｔａｔｉｏｎｓｏｆＣｏｍｐｌｅｘＰｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｔｒｉｃｅｓ￥ＰａｎｇＭｉｎｇｘｉａｎ（逄明贤）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｊｉ...     

A Note on "Rearrangement and Matrix Product Inequalities

ＡＮｏｔｅｏｎ＂ＲｅａｒｒａｎｇｅｍｅｎｔａｎｄＭａｔｒｉｘＰｒｏｄｕｃｔＩｎｅｑｕａｌｉｔｉｅｓ＂ＹａｎｇＺｈｏｎｇｐｅｎｇ（杨忠鹏）（ＤｅｐａｒｔｍｅｎｔＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｊｉｌｉｎ，１３２０１１...     

Strong-principal Bimodules of Jacobson Radical of CSL Algebras

Ｓｔｒｏｎｇ－ｐｒｉｎｃｉｐａｌＢｉｍｏｄｕｌｅｓｏｆＪａｃｏｂｓｏｎＲａｄｉｃａｌ　ｏｆＣＳＬＡｌｇｅｂｒａｓＺｈｕＪｕｎ（朱军）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｂｅｉＩｎｓｔｉｔｕｔｅｆｏｒＭａｔｉｏｎａｌｉｔｉｅｓ，Ｅｎｓ...     

TheDistributionofEigenvaluesforPartitionedMatrix

ＴｈｅＤｉｓｔｒｉｂｕｔｉｏｎｏｆＥｉｇｅｎｖａｌｕｅｓｆｏｒＰａｒｔｉｔｉｏｎｅｄＭａｔｒｉｘＬｉＺｈｕｘｉａｎｇ（李竹香）ＰａｎｇＭｉｎｇｘｉａｎ（逄明贤）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＮｏｒｍａｌＣｏｌｅｇｅ，Ｊｉ...     

Completeness of the Metric Space Induced by Finite Measur

ＣｏｍｐｌｅｔｅｎｅｓｓｏｆｔｈｅＭｅｔｒｉｃＳｐａｃｅＩｎｄｕｃｅｄｂｙＦｉｎｉｔｅＭｅａｓｕｒＹｕＪｉａｎｌｉ；（禹建丽）ＪｉｎＪｉａｑｉ；（金家琦）ＷａｎｇＷｅｉ（（王伟）（ＬｕｏｇａｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ）（Ｋａｉｆｅ...     

Jacobson Radicals Graded by G-sets

ＪａｃｏｂｓｏｎＲａｄｉｃａｌｓＧｒａｄｅｄｂｙＧ－ｓｅｔｓＳｕｎＪｉａｎｈｕａ（孙建华）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｔｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，ＹａｎｇｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｙａｎｇｚｈｏｕ，Ｊｉａｎｇｓｕ，２２...     

Multi-Level Spliting Methods Solving Difference Equations

Ｍｕｌｔｉ┐ＬｅｖｅｌＳｐｌｉｔｉｎｇＭｅｔｈｏｄｓＳｏｌｖｉｎｇＤｉｆｅｒｅｎｃｅＥｑｕａｔｉｏｎｓ＊）ＬｉＦｅｎｇ（李锋）ＬｉＲｏｎｇｈｕａ（李荣华）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕ...     

The Strongly Irreducible Operators in Nest Algebras

ＴｈｅＳｔｒｏｎｇｌｙＩｒｒｅｄｕｃｉｂｌｅＯｐｅｒａｔｏｒｓｉｎＮｅｓｔＡｌｇｅｂｒａｓＪｉＹｏｕｑｉｎｇ（纪友清）ａｎｄＪｉａｎｄＣｈｕｎｌａｎ（蒋春澜）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇ...     

Some Spectral Properties of Metapositive Definite Matrice

ＳｏｍｅＳｐｅｃｔｒａｌＰｒｏｐｅｒｔｉｅｓｏｆＭｅｔａｐｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｔｒｉｃｅｓＬｉＺｈｕｘｉａｎｇ（李竹香）ＬｕＨｏｎｇｂｉｎ（吕洪斌）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＴｅａｃｈｅｒ＇ｓＣｏｌｅｇ...     

关于实方阵的几个问题

本文讨论如下内容：１．把有关对称正定（半正定）的一些性质推广到广义正定（半正定）。２．给定ｘ∈Ｒｍ×ｍ，∧为对角阵，求ＡＸ＝ｘ∧在对称半正定矩阵类中解存在的充要条件及一般形式，并讨论了对任意给定的对称正定（半正定）矩阵Ａ，在上述解的集合中求得Ａ，使得     

Computing a Nearest P-Symmetric Nonnegative Definite Matrix Under Linear Restriction

Let $P$ be an $n\times n$ symmetric orthogonal matrix. A real $n\times n$ matrix $A$ is called P-symmetric nonnegative definite if $A$ is symmetric nonnegative definite and $(PA)^T=PA$. This paper is concerned with a kind of inverse problem for P-symmetric nonnegative definite matrices: Given a real $n\times n$ matrix $\widetilde{A}$, real $n\times m$ matrices $X$ and $B$, find an $n\times n$ P-symmetric nonnegative definite matrix $A$ minimizing $||A-\widetilde{A}||_F$ subject to $AX =B$. Necessary and sufficient conditions are presented for the solvability of the problem. The expression of the solution to the problem is given. These results are applied to solve an inverse eigenvalue problem for P-symmetric nonnegative definite matrices.     

Ranks of Solutions of the Matrix Equation AXB = C

The purpose of this article is to solve two problems related to solutions of a consistent complex matrix equation AXB = C : (I) the maximal and minimal ranks of solution to AXB = C , and (II) the maximal and minimal ranks of two real matrices X₀ and X₁ in solution X = X₀ + iX₁ to AXB = C . As applications, the maximal and minimal ranks of two real matrices C and D in generalized inverse (A + iB)^- = C + iD of a complex matrix A + iB are also examined.     

The Inverse Problem of Centrosymmetric Matrices with a Submatrix Constraint

By using Moore-Penrose generalized inverse and the general singular value decomposition of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the centrosymmetric solutions with a submatrix constraint of matrix inverse problem AX = B. In addition, in the solution set of corresponding problem, the expression of the optimal approximation solution to a given matrix is derived.     

More on Electrostatic Models for Zeros of Orthagonal Polynomials

Representations for inverses of Toeplitz-plus-Hankel matrices and more general Bezoutians involving only discrete Hartley transforms and diagonal matrices are presented. Using these representations a column vector can be multiplied by the inverse of a Toeplitz-plus-Hankel matrix with the help of only 6 Hartley transforms plus O(n) operations. This complexity estimate is significantly better than previous ones.     

矩阵方程AX=B的转动不变解及其最佳逼近

利用矩阵的广义逆、奇异值分解、张量积和拉直算子,给出了矩阵方程AX=B有转动不变解的充分必要条件及有解时通解的表达式;给出了矩阵方程解集合中与给定矩阵的最佳逼近解的表达式.     

关于Fuzzy矩阵的Moore-Penrose逆

讨论Fuzzy矩阵的Moore-PenrOSe逆,给出一些Moore-Penrose逆存在的充要条件以及Moore-Penrose逆的划画。     

The Nearest Bisymmetric Solutions of Linear Matrix Equations

The necessary and sufficient conditions for the existence of and the expressions for the bisymmetric solutions of the matrix equations (Ⅰ)A1X1B1 A2X2B2 ^… AkXkBk=D,(Ⅱ)A1XB1 A2XB2 … AkXBk=D and (Ⅲ) (A1XB1,A2XB2,…,AkXBk)=(D1,D2,…,Dk) are derived by using Kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given. Numerical methods and numerical experiments of finding the neaxest solutions axe also provided.     

矩阵方程LX=M与LXK=M的实部有定解

本文利用矩阵的ＭＰ逆与奇异值分解作为工具,给出了矩方程ＬＸ＝Ｍ与ＬＸＫ＝Ｋ存在实部有定解的充要条件以及这种解的一般形式。     

几种矩阵逆的连续性

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．