| 二次广义Hermite矩阵方程的解 |
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| 引用本文： | 袁晖坪.二次广义Hermite矩阵方程的解[J].吉林大学学报(理学版),2012,50(2):281-283. |
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| 作者姓名： | 袁晖坪 |
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| 作者单位： | 重庆工商大学 数学与统计学院, 重庆 400067 |
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| 基金项目： | 重庆市自然科学基金(批准号:CSTS2005BB0243);重庆市教委科技项目基金(批准号:KJ0707023) |
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| 摘 要： | 利用广义Hermite矩阵探讨一类二次矩阵方程的求解问题, 得到了矩阵方程XAX=A存在广义Hermite矩阵解的充分必要条件及其相应解的表达式, 并给出了矩阵方程XAY=B当A,B可逆时的通解表达式.
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| 关 键 词： | 广义Hermite矩阵 二次矩阵方程 矩阵解 通解 |
| 收稿时间： | 2011-08-22 |
Solutions of Quadratic Generalized Hermite Matrix Equation |
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| YUAN Hui-ping.Solutions of Quadratic Generalized Hermite Matrix Equation[J].Journal of Jilin University: Sci Ed,2012,50(2):281-283. |
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| Authors: | YUAN Hui-ping |
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| Institution: | College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China |
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| Abstract: | The solutions of quadratic matrix equation were discuss ed via the generalized Hermite matrix.The findings show that there are necessar y and sufficient conditions of matrix equation XAX=A having their generalized Hermite matrix solution,and the simple expressions of the generalized Hermite matrix solution can also be obtained.Besides,the ge neral solutions of the matrix equations XAY=B were given. |
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| Keywords: | generalized Hermite matrix quadratic matrix equatio n matrix solution general solution |
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