矩阵乘积的正定性 |
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引用本文: | 詹仕林. 矩阵乘积的正定性[J]. 安徽大学学报(自然科学版), 2003, 27(2): 10-12 |
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作者姓名: | 詹仕林 |
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作者单位: | 韩山师范学院,数学系,广东,潮州,521041 |
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摘 要: | 两个正定矩阵的和必是正定矩阵,但其积则未必是正定矩阵.本文对两个实矩阵的乘积为正定矩阵的问题进行探讨,给出了某些实矩阵的积为正定矩阵的一系列充要条件.作为应用,给出了KyFanTaussky定理的一个简捷的证明方法.
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关 键 词: | 正定对称矩阵 正定矩阵 充分必要条件 |
文章编号: | 1000-2162(2003)02-0010-03 |
On the positive definiteness of the product of matrices |
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Abstract: | The sum of two positive definite matrices is sure a positive definite matix,but their product may not. In this paper,we discuss the condition that two matrices product is a positive definite matrix and give a series of necessary and sufficient conditions.On the application, a simple and convenient testimony is given for the Key Fan Taussky'Theory. |
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Keywords: | positive definite symmetric matrix positive definite matrix necessary and sufficient condition |
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