THE SOLVABILITY CONDITIONS FOR INVERSE EIGENVALUE PROBLEM OF ANTI-BISYMMETRIC MATRICES

• 来源期刊: 计算数学(英文版)
• 关键词: Eigenvalue problem Norm Approximate solution.
• 年，卷（期）: 2002,（3）
• 页码范围: 245-256
• 页数: 12页
• 语种: 英文

摘要

This paper is mainly concerned with solving the following two problems: Problem Ⅰ.Given X ∈Cn×m,(A)=diag(λ1，λ2…,λm)∈Cm×m.Find A∈ABSRn×n such that AX = XA where ABSRn×n is the set of all real n × n anti-bisymmetric matrices. Problem Ⅱ. Given A* ∈ Rn×n. Find (A^) ∈ SE such that ‖A*-(A^)‖F=min A∈SE‖A*-A‖F, where ‖ @ ‖F is Frobenius norm, and SE denotes the solution set of Problem I.The necessary and sufficient conditions for the solvability of Problem Ⅰ have been stud-ied. The general form of SE has been given. For Problem Ⅱ the expression of the solutionhas been provided.