| 矩阵方程aX2+bX+cE=O的正定解和实对称解 |
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| 引用本文： | 蒋永泉.矩阵方程aX2+bX+cE=O的正定解和实对称解[J].大学数学,2005,21(2):113-115. |
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| 作者姓名： | 蒋永泉 |
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| 作者单位： | 徐州师范大学,数学系,徐州,221116 |
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| 摘 要： | 给出了矩阵方程aX2+bX+cE=O,a,b,c∈R,a≠0有正定解,实对称解的充分必要条件及解的一般形式.
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| 关 键 词： | 矩阵方程 正定解 对称解 特征方程 特征值 |
| 文章编号： | 1672-1454(2005)02-0113-03 |
| 修稿时间： | 2004年2月16日 |
The Positive Definite Solution and the Real Symmetric Solution of the Matrix Equation aX2+bX+cE=O |
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| JIANG Young-quan.The Positive Definite Solution and the Real Symmetric Solution of the Matrix Equation aX2+bX+cE=O[J].College Mathematics,2005,21(2):113-115. |
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| Authors: | JIANG Young-quan |
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| Abstract: | In this paper, the necessary and sufficient conditions are given for the matrix equation aX~2+bX+cE=O have positive definite solutions or real symmetric solutions. Moreover, the positive definite solution and the real symmetric solution, if exist, are described completely. |
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| Keywords: | matrix equation positive definite solution real symmetric solution characteristic equation eigenvalue |
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