| 矩阵方程X+A*X-2A=I有对称正定解的充分必要条件 |
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| 引用本文： | 程明松.矩阵方程X+A*X-2A=I有对称正定解的充分必要条件[J].北京大学学报(自然科学版),2005,41(1):55-61. |
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| 作者姓名： | 程明松 |
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| 作者单位： | 北京大学数学科学学院,北京,100871 |
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| 摘 要： | 给出了矩阵方程X A^*X^-2A=I有对称正定解的两个充分必要条件，它们在算法设计和理论分析上可能有一定的用途。根据这两个定理，当矩阵方程有对称正定解时，给出了系数矩阵A必须满足的条件，这些条件大部分都是很容易验证的。
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| 关 键 词： | 非线性矩阵方程 对称正定解 充分必要条件 |
Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution of the Matrix Equation X+A*X-2A=I |
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| CHENG Mingsong.Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution of the Matrix Equation X+A*X-2A=I[J].Acta Scientiarum Naturalium Universitatis Pekinensis,2005,41(1):55-61. |
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| Authors: | CHENG Mingsong |
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| Abstract: | The matrix equation X A*X -2A=I is studied.Some necessary and sufficient conditions for the existence of a positive definite solution of this equation are derived.Based on them,some properties of the coefficient matrix A are presented when the matrix equation has a positive definite solution. |
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| Keywords: | nonlinear matrix equation positive definite solution necessary and sufficient condition |
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