| 矩阵方程AX=B,XC=D的定秩解 |
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| 引用本文： | 肖庆丰.矩阵方程AX=B,XC=D的定秩解[J].数学杂志,2016,36(3):458-464. |
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| 作者姓名： | 肖庆丰 |
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| 作者单位： | 东莞职业技术学院基础课部, 广东 东莞 523808 |
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| 基金项目： | Supported by Scientiflc Research Fund of Dongguan Polytechnic (2012a03). |
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| 摘 要： | 本文研究了一类矩阵方程组解的秩的范围.利用矩阵的奇异值分解以及Frobenius范数的特征,得到了解的极值秩以及解的通式,并就这些问题的特殊情况进行了讨论,得到了一些结果.
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| 关 键 词： | 最优控制 极值秩 奇异值分解 Frobenius范数 |
| 收稿时间： | 2013/10/8 0:00:00 |
| 修稿时间： | 2013/12/10 0:00:00 |
THE EXTREMAL RANK SOLUTIONS OF THE MATRIX EQUATIONS AX = B, XC = D |
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| XIAO Qing-feng.THE EXTREMAL RANK SOLUTIONS OF THE MATRIX EQUATIONS AX = B, XC = D[J].Journal of Mathematics,2016,36(3):458-464. |
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| Authors: | XIAO Qing-feng |
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| Institution: | Department of Basic, Dongguan Polytechnic, Dongguan 523808, China |
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| Abstract: | In this paper, we considered the rank range of the solutions of a class of matrix equations. By applying the singular value decomposition of matrix and the properties of Frobenius matrix norm, we obtained the extremal rank and the solution expression of under rank constrained. Some special cases of theses problems are considered, and some results are obtained. |
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| Keywords: | optimal control extremal rank SVD decomposition Frobenius matrix norm |
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