| 矩阵分解及其求逆矩阵 |
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| 引用本文： | 龚爱玲.矩阵分解及其求逆矩阵[J].天津理工大学学报,1995(3). |
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| 作者姓名： | 龚爱玲 |
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| 作者单位： | 天津理工学院计算机工程与数学系 |
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| 摘 要： | Ｄｏｏｌｉｔｔｌｅ对矩阵分解为在矩阵的各阶主子矩阵为非奇异的条件下，Ａ可唯一的分解为一个下三角分块矩阵与一个上三角分块矩阵的乘积形式，本文给出若矩阵Ａ的左上主子矩阵有一个ｒ阶主子矩阵为非奇异的，则Ａ可分解为一个下三角分块矩阵与一个上三角分块矩阵的乘积形式，并给出求逆的计算方法。
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| 关 键 词： | 逆矩阵，初等变换，三角矩阵，满秩矩阵，分块矩阵 |
THE RESOLUTION OF THE MATRIX AND SOLUTION OF THE INVERSE MATRIX |
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| Gong Ailing.THE RESOLUTION OF THE MATRIX AND SOLUTION OF THE INVERSE MATRIX[J].Journal of Tianjin University of Technology,1995(3). |
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| Authors: | Gong Ailing |
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| Institution: | Gong Ailing |
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| Abstract: | The method of Doolittle resolve matris is as follows:Under the non-peculiarcondition in the main factor matrix of everystep of the matrix. A is the only one to resolvethe form of the product of a down triangle matrix in pieces and an up triangle matrix inpieces.The article comes to the conclusion that if in the upper left main factor matrix ofmatrix exists a main factor matrix of r step peculiar,then A can be resolved as the form ofthe product of a down triangle matrix in pieces and an upper triangle matrix in pieces. Thearticle also presents the calculated mathod to seek the solution of its matris form. |
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| Keywords: | inverse matrix elementary operation triangle matrix full rand matrix matrix in pieces |
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