| 矩阵方程AXB=C的最小二乘解的定秩研究 |
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| 引用本文： | 孟纯军,李桃珍. 矩阵方程AXB=C的最小二乘解的定秩研究[J]. 湖南大学学报(自然科学版), 2013, 40(7): 92-94 |
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| 作者姓名： | 孟纯军 李桃珍 |
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| 作者单位： | 湖南大学数学与计量经济学院,湖南长沙,410082 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 研究了矩阵方程AXB=C最小二乘解的秩的范围,利用矩阵的奇异值分解以及Frobenius范数的特征,得到了秩约束下最小二乘解的表达式,并得到了最大秩和最小秩最小二乘解.
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| 关 键 词： | 最优控制 最小二乘解 秩约束 奇异值分解 Frobenius范数 |
On the Rank Range of the Least-squares Solutions of the Matrix Equation AXB=C |
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| MENG Chun-jun,LI Tao-zhen. On the Rank Range of the Least-squares Solutions of the Matrix Equation AXB=C[J]. Journal of Hunan University(Naturnal Science), 2013, 40(7): 92-94 |
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| Authors: | MENG Chun-jun LI Tao-zhen |
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| Affiliation: | (College of Mathematics and Econometrics, Hunan Univ, Changsha, Hunan410082, China) |
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| Abstract: | This paper, we considered the rank range of the least-squares solutions of matrix equation AXB=C. By applying the singular value decomposition of matrix and the properties of Frobenius matrix norm, we have obtained the range of the rank and the least-squares solution expression of under rank constrained. Finally, we have provided the expressions of the least-squares solutions with maximal and minimum rank respectively. |
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| Keywords: | optimal control least-squares solutions rank constrained SVD decomposition Frobenius norm |
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