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矩陣反問(wèn)題初探
矩陣反問(wèn)題初探
摘要
本文提出了伴隨矩陣的反問(wèn)題,根據(jù)矩陣的有關(guān)知識(shí)導(dǎo)出了該反問(wèn)題有解的充分必要條件,并給出了解的個(gè)數(shù)。另外考慮了實(shí)對(duì)稱矩陣的特征值反問(wèn)題,在解決該反問(wèn)題的同時(shí)給出了該問(wèn)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(xiàng)。最后,淺談了矩陣逆特征值問(wèn)題的應(yīng)用。
關(guān)鍵詞:伴隨矩陣;實(shí)對(duì)稱矩陣;特征值反問(wèn)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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