矩陣反問題初探

矩陣反問題初探

矩陣反問題初探
 
摘要

本文提出了伴隨矩陣的反問題，根據矩陣的有關知識導出了該反問題有解的充分必要條件，并給出了解的個數。另外考慮了實對稱矩陣的特征值反問題，在解決該反問題的同時給出了該問題有解的充分條件。為更深入地理解此充分條件，討論了它的注意事項。最后，淺談了矩陣逆特征值問題的應用。
關鍵詞：伴隨矩陣;實對稱矩陣;特征值反問題 
            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.

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