一类矩阵反问题解存在的条件

THE SOLVABILITY CONDITIONS FOR THE INVERSE PROBLEM OF MATRICES

矩阵反问题在自动控制、振动理论、土木工程和经济等领域中有着广泛应用。目前 ,在Jacobi矩阵反问题、实对称带状矩阵反问题等方面取得了一定的进展 [参考文献 1]。研究了反对称矩阵反问题 。

Matrix Inverse Problem has wide application in automatic controlling,Vibration Theory,Civil Engineering and Economics.The following problems A: Given X,B∈R n×n ,finding A∈ASR n×n such as:AX=B here ASR=｛A∈R n×n ｜A=-A T｝are considered.The necessary and sufficient condition about the problem are derived,The expression of the solution is provided.