| 乘积矩阵为对角占优阵的充分和必要条件 |
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| 引用本文： | 伍国兴. 乘积矩阵为对角占优阵的充分和必要条件[J]. 东北林业大学学报, 2008, 36(8) |
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| 作者姓名： | 伍国兴 |
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| 作者单位： | 东北林业大学,哈尔滨,150040 |
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| 摘 要： | 用向量的内积、矩阵的迹及矩阵范数等给出了矩阵乘积为对角占优阵的充分和必要条件,特别给出ATA为对角占优阵的充分和必要条件。
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| 关 键 词： | 对角占优阵 矩阵范数 向量内积 |
Necessary and Sufficient Conditions for Products of Two Matrices Being Diagonal Dominant |
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| Wu Guoxing. Necessary and Sufficient Conditions for Products of Two Matrices Being Diagonal Dominant[J]. Journal of Northeast Forestry University, 2008, 36(8) |
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| Authors: | Wu Guoxing |
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| Abstract: | It is well-known that most iterative methods converge for linear systems whose coefficient matrix is diagonal dominant.Some necessary and sufficient conditions for products of two matrices being diagonally dominant are given by using inner product of vectors,trace of matrices and the norm of matrices,especially for matrix ATA. |
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| Keywords: | Diagonal dominant matrix Matrix norm Inner product |
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