| 矩阵方程AXB+CYD=E的Toeplitz矩阵解 |
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| 引用本文： | 孙庆娟,郭文彬,王柄中. 矩阵方程AXB+CYD=E的Toeplitz矩阵解[J]. 河南科技大学学报(自然科学版), 2012, 33(3): 93-97,115 |
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| 作者姓名： | 孙庆娟 郭文彬 王柄中 |
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| 作者单位： | 聊城大学数学科学学院,山东聊城,252059 |
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| 摘 要： | 利用矩阵的Kronecker积、矩阵的拉直算子和Moore-Penrose广义逆的有关知识,给出了矩阵方程AXB+CYD=E的Toeplitz矩阵解和对称Toeplitz矩阵解的表达式,并给出了其最小二乘解的一般形式。
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| 关 键 词： | Toeplitz矩阵 Kronecker积 矩阵的拉直算子 Moore-Penrose广义逆 |
Toeplitz Matrix Solutions of Matrix Equation AXB+CYD=E |
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| SUN Qing-Juan,GUO Wen-Bin,WANG Bing-Zhong. Toeplitz Matrix Solutions of Matrix Equation AXB+CYD=E[J]. Journal of Henan University of Science & Technology:Natural Science, 2012, 33(3): 93-97,115 |
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| Authors: | SUN Qing-Juan GUO Wen-Bin WANG Bing-Zhong |
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| Affiliation: | (School of Mathematics Science,Liaocheng University,Liaocheng 252059,China) |
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| Abstract: | The expressions of the Toeplitz matrix solution and symmetric Toeplitz matrix solution of the matrix equation AXB+CYD=E were given in this paper by using the Kronecker product of matrices,matrices straight operator and Moore-Penrose generalized inverse.And also the expressions of the least squares solution was given. |
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| Keywords: | Toeplitz matrix Kronecker product Matrix straight operator Moore-Penrose generalized inverse |
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