| 线性流形上矩阵方程的对称次反对称最小二乘解 |
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| 引用本文： | 钱爱林,艾国荣.线性流形上矩阵方程的对称次反对称最小二乘解[J].咸宁学院学报,2009,29(3):1-4. |
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| 作者姓名： | 钱爱林 艾国荣 |
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| 作者单位： | 1. 咸宁学院,数学与统计学院,湖北,咸宁,437000
2. 咸宁市温泉中学,湖北,咸宁,437000 |
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| 摘 要： | 设矩阵A=（aij）∈R^n×n，如果满足aij=aji=-an-j＋1,n-i-4（i,j=1，2，…，n），则称A为对称次反对称矩阵，所有n阶对称次反对称矩阵的全体记为SASR^n×n ．本文通过矩阵的广义奇异值分解，得到了线性流形上矩阵方程A^TXA=B存在对称次反对称解的充分必要条件，并且给出了解的表达式及其最佳逼近的条件．
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| 关 键 词： | 矩阵方程 对称次反对称矩阵 奇异值分解 最佳逼近 |
The Symmetric and Sub- Anti- Symmetric Solutions of the Linear Matrix Equation on some Linear Manifolds |
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| QIAN Ai-lin,AI Guo-rong.The Symmetric and Sub- Anti- Symmetric Solutions of the Linear Matrix Equation on some Linear Manifolds[J].Journal of Xianning College,2009,29(3):1-4. |
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| Authors: | QIAN Ai-lin AI Guo-rong |
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| Institution: | QIAN Ai -lin, AI Guo - rong (1. College of Mathematics and Statistics,Xianning University ,Xianning 437100 ,China 2. Xianning Experimental Middle School; Xianning 437100, China) |
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| Abstract: | By applying the generalized singular value decomposition of matrices, this paper provides the necessary and sufficient conditions for the existence and the expression of the symmetric and sub - anti - symmet- ric solutions of the linear matrix equation on some linear manifolds. In addition, the expression of the optimal approximation solution to the given matrix is derived. |
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| Keywords: | Matrix Equation Symmetric and Sub -Anti- Symmetric Matrices Optimal Approximation |
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