| 子阵约束下矩阵方程AX=B反问题的实反对称解及其最佳逼近 |
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| 引用本文： | 陈亚波. 子阵约束下矩阵方程AX=B反问题的实反对称解及其最佳逼近[J]. 湖南农业大学学报(自然科学版), 2002, 28(5): 444-446 |
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| 作者姓名： | 陈亚波 |
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| 作者单位： | 湖南农业大学理学院,湖南,长沙,410128 |
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| 摘 要： | 利用矩阵的奇异值分解及广泛逆，给出了子矩阵约束下矩阵方程AX＝B反问题有实反对称解的充分必要条件及其通解的表达式，另外，给出了解集合中与给定矩阵的最佳逼近解的表达式以及求解最佳逼近解的一个数值算法和一个数值例子。
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| 关 键 词： | 子阵约束 矩阵方程 实反对称解 反对称矩阵 反问题 最佳逼近 广义逆 数值算法 |
| 文章编号： | 1007-1032(2002)05-0444-03 |
| 修稿时间： | 2002-04-03 |
Real Anti-Symmetric Solutions of Inverse Problem of the Matrix Equation AX=B under a Submatrix Constraint and Its Optimal Approximation |
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| CHEN Ya-bo. Real Anti-Symmetric Solutions of Inverse Problem of the Matrix Equation AX=B under a Submatrix Constraint and Its Optimal Approximation[J]. Journal of Hunan Agricultural University, 2002, 28(5): 444-446 |
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| Authors: | CHEN Ya-bo |
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| Abstract: | Inverse probles of matricem have been widely used in fields of structure design and automatic control .By using the singular value decomposition (SVD)and Moore-Penrose inverse of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the anti-symmetric solutions of inverse problem of the matrix equation AX = B under a submatrix constraint. In addition, in the solution set of corresponding problem, the expression of the optimal approximation solution to a given matrix is derived,and a numerical algorithm and a numerical example for solving optimal approximation solution are included. |
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| Keywords: | anti-symmetric matrix inverse problem optimal approximation |
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