| 子矩阵约束下反对称正交反对称矩阵反问题及其最佳逼近 |
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| 引用本文： | 熊培银,李学峰,李治.子矩阵约束下反对称正交反对称矩阵反问题及其最佳逼近[J].海南大学学报(自然科学版),2008,26(3):236-240. |
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| 作者姓名： | 熊培银 李学峰 李治 |
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| 作者单位： | 仰恩大学,数学系,福建,泉州,362014 |
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| 基金项目： | 仰恩大学社科研究规划资助课题 |
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| 摘 要： | 利用矩阵的奇异值分解和矩阵对的商奇异值分解，讨论了子矩阵约束下反对称正交反对称矩阵的反问题，给出了其有解的充分必要条件及在有解条件下的通解表达式，并得到了此问题的最佳逼近解，给出了求最佳逼近解的数值算法及数值算例，验证了方法的有效性．
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| 关 键 词： | 反对称正交反对称矩阵 反对称矩阵 商奇异值分解 最佳逼近 |
The Inverse Problem of Anti-bisymmetric Anti-orth-symmetric Matrices with a Sub-matrix Constraint |
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| XIONG Pei-yin,LI Xue-feng,LI Zhi.The Inverse Problem of Anti-bisymmetric Anti-orth-symmetric Matrices with a Sub-matrix Constraint[J].Natural Science Journal of Hainan University,2008,26(3):236-240. |
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| Authors: | XIONG Pei-yin LI Xue-feng LI Zhi |
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| Institution: | (Department of Mathematics, Yang En University, Quanzhou 362014, China ) |
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| Abstract: | By applying the singular value decomposition and the quotient singular value decomposition, the inverse problem of anti-bisymmetric anti-orth-bisymmetric matrices with a sub-matrix constraint was studied firstly. Second, the sufficient and necessary conditions and the general solutions of the problem are provided and the optimal approximate solution is given. Finally, numeral algorithm and example are given to show the effectiveness of the proposed method. |
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| Keywords: | anti-bisymmetric anti-orth-bisymmetric matrices anti-symmetric matrices quotient singular value decomposition optimal approximation |
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