| 求逆矩阵的一个递推公式 |
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| 引用本文： | 赵国枝.求逆矩阵的一个递推公式[J].中北大学学报,1989(3). |
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| 作者姓名： | 赵国枝 |
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| 摘 要： | 本文由解微分方程组K(t)=AX(t),求A的特征矩阵之逆(SI—A)~(-1) 的过程,导出求n阶矩阵A之逆的一个递推公式.利用本公式求n阶矩阵的逆,只要简单地计算n次两个矩阵之积和n次两个矩阵之差即可,避开了计算伴随矩阵和行列式的麻烦。方法简单,运算过程规律,和其它求逆方法比较还具有精度高的特点,适合于高阶矩阵之逆,更便于上机计算。
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| 关 键 词： | 逆矩阵 特征矩阵 拉普拉斯变换 |
A RECURRENCE FORMULA FOR COMPUTING INVERSE MATRIX |
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| Zhao Guozhi.A RECURRENCE FORMULA FOR COMPUTING INVERSE MATRIX[J].Journal of North University of China,1989(3). |
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| Authors: | Zhao Guozhi |
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| Affiliation: | Zhao Guozhi |
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| Abstract: | This paper introduces a recurrence formula for computing inverse matrix A~(-1) that derive itself from the solution of linear differential equations X(t)=AX(t) and finding the inverse of ei- genvalue matrix (SI-A)~(-1). When this method is applied to solve the n-order inverse matrix, it is only required to compute the product of two matrices n times and the difference of two matrices n times, thus the troubles on computing the determinant and the adjugate matrix are averted. This method is easy to be completed on compu- ter, and applicable to solve the inverse of high-order matrices. |
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| Keywords: | inverse matrix characteristic matrix Laplace transform |
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