矩阵反问题初探

矩阵反问题初探

摘要

本文提出了伴随矩阵的反问题，根据矩阵的有关知识导出了该反问题有解的充分必要条件，并给出了解的个数。另外考虑了实对称矩阵的特征值反问题，在解决该反问题的同时给出了该问题有解的充分条件。为更深入地理解此充分条件，讨论了它的注意事项。最后，浅谈了矩阵逆特征值问题的应用。

关键词：伴随矩阵;实对称矩阵;特征值反问题

The Origin exploration of inverse Problems of Matrices

ABSTRACT

In this paper, the inverse problem of adjoint was firstly considered. The necessary and sufficient conditions of solvability for the problem were derived according to concerned knowledge about matrices and the number of general solution was given. Then we investigated the inverse eigenvalue problem of real symmetric matrices. The inverse problem was solved and meanwhile gave the sufficient conditions for this problem. Something about the sufficient conditions, which was worth noticing, was discussed so as to be understood deeply. Finally, we simply talk about the application and development of inverse eigenvalue problem.

Key words: adjoint; real symmetric matrices; eigenvalue inverse problem.