| 一个来自振动理论反问题的矩阵方程 |
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| 引用本文： | 吴筑筑,王国荣.一个来自振动理论反问题的矩阵方程[J].高校应用数学学报(英文版),2003,18(1):77-82. |
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| 作者姓名： | 吴筑筑 王国荣 |
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| 作者单位： | Wu Zhuzhu Wang Guorong Dept. of Computer，Shaoguan Univ.，Guangdong Shaoguan 512005，China. College of Math.Sciences，Shanghai Normal Univ.，Shanghai 200234，China. |
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| 基金项目： | NationalNaturalScienceFoundationofChina(199710 5 7)andScienceandTechnologyFoundationofShanghaiandShanghaiHigherEducationProject (0 0JC140 5 7) . |
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| 摘 要： | § 1 ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＲｎ×ｍｄｅｎｏｔｅｔｈｅｒｅａｌｎ×ｍｍａｔｒｉｘｓｐａｃｅ ,Ｒｎ×ｍｒ ｉｔｓｓｕｂｓｅｔｗｈｏｓｅｅｌｅｍｅｎｔｓｈａｖｅｒａｎｋｒ ,ＯＲｎ×ｎｔｈｅｓｅｔｏｆａｌｌｎ×ｎｏｒｔｈｏｇｏｎａｌｍａｔｒｉｃｅｓ,ＳＲｎ×ｎ(ＳＲｎ×ｎ≥ ,ＳＲｎ×ｎ>)ｔｈｅｓｅｔｏｆａｌｌｎ×ｎｒｅａｌｓｙｍｍｅｔｒｉｃ (ｓｙｍｍｅｔｒｉｃｐｏｓｉｔｉｖｅｓｅｍｉｄｅｆｉｎｉｔｅ ,ｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅ)ｍａｔｒｉｃｅｓ.ＴｈｅｎｏｔａｔｉｏｎＡ>0 (≥ 0 ,<0 ,≤ 0 )ｍ…
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| 收稿时间： | 22 February 2002 |
A matrix equation from an inverse problem of vibration theory |
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| Wu?Zhuzhu,Wang?Guorong.A matrix equation from an inverse problem of vibration theory[J].Applied Mathematics A Journal of Chinese Universities,2003,18(1):77-82. |
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| Authors: | Wu Zhuzhu Wang Guorong |
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| Institution: | (1) Dept. of Computer, Shaoguan Univ., 512005 Guangdong, Shaoguan, China;(2) College of Math. Sciences, Shanghai Normal Univ., 200234 Shanghai, China |
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| Abstract: | The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived. |
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| Keywords: | matrix equation symmetric matrix positive semidefinite matrix positive definite matrix generalized inverse matrix |
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