This paper discuss the following two problems:Problem I. Given . Find A,such thatAX=XA,where BSRn×n is the set of all n × n bisymmetric matrices.Problem II. Given Find A SE such that where SE is the solution...This paper discuss the following two problems:Problem I. Given . Find A,such thatAX=XA,where BSRn×n is the set of all n × n bisymmetric matrices.Problem II. Given Find A SE such that where 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. Then expression of the solution A of Problem II is presented.展开更多
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
A = （aij） Rn×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSRn×n Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Pro...A = （aij） Rn×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSRn×n Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Problem Ⅰ. Given X Rn×m, B Rn×m. Find A S such that Problem Ⅱ. Given A* E Rn×n. Find A SE such that Where is Frobenius norm, and SE is the solution set of Problem I. In this paper the general representation of SE has been given. The necessary and sufficient conditons have been presented for Problem I0. For Problem Ⅱ the expression of the solution has been provided.展开更多
文摘This paper discuss the following two problems:Problem I. Given . Find A,such thatAX=XA,where BSRn×n is the set of all n × n bisymmetric matrices.Problem II. Given Find A SE such that where 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. Then expression of the solution A of Problem II is presented.
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A = （aij） Rn×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSRn×n Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Problem Ⅰ. Given X Rn×m, B Rn×m. Find A S such that Problem Ⅱ. Given A* E Rn×n. Find A SE such that Where is Frobenius norm, and SE is the solution set of Problem I. In this paper the general representation of SE has been given. The necessary and sufficient conditons have been presented for Problem I0. For Problem Ⅱ the expression of the solution has been provided.
