| 一类线性流形上矩阵方程X^TAX=B的反问题 |
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| 引用本文： | 郁金祥. 一类线性流形上矩阵方程X^TAX=B的反问题[J]. 数学理论与应用, 2008, 28(2): 38-42 |
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| 作者姓名： | 郁金祥 |
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| 作者单位： | 嘉兴学院数学与信息工程学院 嘉兴，314001 |
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| 摘 要： | 设Ω={A∈ASR^nxn｜Ax=C，↓Ax∈RT（S），SS^＋C=0，T2^TC2=-C2^TT2，C2T2^＋72=C2}，考虑问题Ⅰ：给定X∈R^nxm，B∈R^mxm求A∈Ω，使得f（A）=｜｜X^TAX—B｜｜=min；问题Ⅱ：给定A^＋∈R^nxm，求A∈SE，使得｜｜A^＋-A｜｜=minA∈SE｜｜A^＋-A｜｜，SE是问题Ⅰ的解集。本文给出了问题Ⅰ、Ⅱ的解的通式，并给出了问题Ikf（A）=0成立的充分必要条件。
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| 关 键 词： | 线性流形 反对称矩阵 反问题 |
The Inverse Problems of Matrices Equation B~TAX=B on A Class of Linear Manifold |
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| Yu Jinxing. The Inverse Problems of Matrices Equation B~TAX=B on A Class of Linear Manifold[J]. Mathematical Theory and Applications, 2008, 28(2): 38-42 |
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| Authors: | Yu Jinxing |
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| Affiliation: | Yu Jinxing ( College of mathematics and information science, Jiaxin University, Jiaxin, 314001 ) |
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| Abstract: | Let Ω={A∈ASR^nxn｜Ax=C,↓Ax∈RT（S）,SS^＋C=0,T2^TC2=-C2^TT2,C2T2^＋72=C2},This paper considers the problem Ⅰ：Given X∈R^nxm,B∈R^mxm find A∈Ω such thatf（A）=｜｜X^TAX-B｜｜=min; and considers the problem Ⅱ：Given A^＋∈R^nxm,find A∈SE ,such that ｜｜A^＋-A｜｜=minA∈SE｜｜A^＋-A｜｜ ,where SE denotes the solution set of Problem Ⅰ. The expressions for general solutions of the Problem I.n are given, and the necessary and sufficient condition for the existence of a solution to Problem Ⅰ is studied. |
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| Keywords: | linear manifold anti-symmetric inverse problem |
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