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矩陣直積與拉直算子的有關(guān)性質(zhì)及應用
矩陣直積與拉直算子的有關(guān)性質(zhì)及應用
摘要
本文介紹了矩陣直積的有關(guān)概念和性質(zhì),利用矩陣直積和拉直算子給出了線(xiàn)性矩陣方程有解的充分必要條件以及有惟1解的充分必要條件.然后將這些定理應用于解3種形式的線(xiàn)性矩陣方程.本文還討論了矩陣直積和拉直算子在解矩陣微分方程中的1點(diǎn)應用,同時(shí)給出了矩陣微分方程解的形式.
關(guān)鍵詞： 矩陣直積； 矩陣的拉直； 線(xiàn)性矩陣方程 ； 矩陣微分方程
The properties and applications of matrix direct product and straight operator
ABSTRACT
In this paper, some concepts and characters about matrix direct product have been introduced. With the matrix direct product and straightening operator, the necessary and sufficient conditions of the linear matrix equations have solutions and have unique one solution are given. Using these results, three types of Linear matrix equations are solved. In addition, in this paper, some applications of matrix direct product and straightening operator to solve matrix differential equations are discussed. And a matrix form solution of matrix differential equations is given.
Key words: matrix product; matrix realligned; Linear matrix equation; Matrix differential equation
目 錄
中文標題………………………………………………………………………………………1
中文摘要、關(guān)鍵詞……………………………………………………………………………1
英文標題………………………………………………………………………………………1
英文摘要、關(guān)鍵詞……………………………………………………………………………1
正文
1 引 言…………………………………………………………………………………2
2 矩陣直積有關(guān)概念及性質(zhì) …………………………………………………………3
2.1 矩陣直積的基本性質(zhì) …………………………………………………………………3
2.2 矩陣直積的特征值、特征向量及行列式 …………………………………5
2.2 矩陣拉直有關(guān)概念及性質(zhì) …………………………………………………8
3 矩陣直積的應用……………………………………………………………………………9
3.1 矩陣直積求解線(xiàn)性矩陣方程的應用 …………………………………………………9
3.2 矩陣直積求解矩陣微分方程的應用 …………………………………………………17
4 結束語(yǔ)……………………………………………………………………………………18
參考文獻………………………………………………………………………………………19
致謝……………………………………………………………………………………………20
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