A=（aij） ∈Rn×n is termed bisymmetric matrix if We denote the set of all n × n bisymmetric matrices by BSRn×n In this paper, we discuss the following two problems: Problem I. Given X, Find such that Pr...A=（aij） ∈Rn×n is termed bisymmetric matrix if We denote the set of all n × n bisymmetric matrices by BSRn×n In this paper, we discuss the following two problems: Problem I. Given X, Find such that Problem Ⅱ. Gived . Find such that where ||·|| is Frobenius norm, and SE is the solution set of Problem I. The general form of SE has been given. The necessary and sufficient conditions have been studied for the special cases AX = B and AX = XA of problem I. For problem Ⅱ the expression of the solution has been provided.展开更多
In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag（λ1,…, λm） > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetri...In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag（λ1,…, λm） > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetric nonnegative definite matrices. Problem Ⅱ. Given A* ∈ Rnxn, find ALS ∈ SE such that||A*-ALS||=inf||A*-A|| where SE is the solution set of problem Ｉ. The existence of the solution for problem Ⅰ, Ⅱ and the uniqueness of the solution for Problem Ⅱ are proved. The general form of SE is given and the expression of ALS is presented.展开更多
This paper considers the following two problems:Problem I： Give X, B∈R^n×m, find A∈SAR^n×n such that AX = B Where SAR^n×n is the set of all n×n symmetric and sub-anti-symmetric matrices. Problem...This paper considers the following two problems:Problem I： Give X, B∈R^n×m, find A∈SAR^n×n such that AX = B Where SAR^n×n is the set of all n×n symmetric and sub-anti-symmetric matrices. Problem Ⅱ: Give A^～∈R^n×n find A^∈ SE such that ‖A^～-A^‖= minA∈SE‖A^～-A‖ Where SE is the solution set of problem I, ‖·‖ is the Frobenius norm. The necessary and sufficient conditions are studied for the set SE to be nonempty set, the general form of SE is given. For problem II, the expression of the solutionis provided.展开更多
文摘A=（aij） ∈Rn×n is termed bisymmetric matrix if We denote the set of all n × n bisymmetric matrices by BSRn×n In this paper, we discuss the following two problems: Problem I. Given X, Find such that Problem Ⅱ. Gived . Find such that where ||·|| is Frobenius norm, and SE is the solution set of Problem I. The general form of SE has been given. The necessary and sufficient conditions have been studied for the special cases AX = B and AX = XA of problem I. For problem Ⅱ the expression of the solution has been provided.
文摘In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag（λ1,…, λm） > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetric nonnegative definite matrices. Problem Ⅱ. Given A* ∈ Rnxn, find ALS ∈ SE such that||A*-ALS||=inf||A*-A|| where SE is the solution set of problem Ｉ. The existence of the solution for problem Ⅰ, Ⅱ and the uniqueness of the solution for Problem Ⅱ are proved. The general form of SE is given and the expression of ALS is presented.
文摘This paper considers the following two problems:Problem I： Give X, B∈R^n×m, find A∈SAR^n×n such that AX = B Where SAR^n×n is the set of all n×n symmetric and sub-anti-symmetric matrices. Problem Ⅱ: Give A^～∈R^n×n find A^∈ SE such that ‖A^～-A^‖= minA∈SE‖A^～-A‖ Where SE is the solution set of problem I, ‖·‖ is the Frobenius norm. The necessary and sufficient conditions are studied for the set SE to be nonempty set, the general form of SE is given. For problem II, the expression of the solutionis provided.
