| MATRIX EQUATION AXB = E WITH PX = sXP CONSTRAINT |
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| 作者姓名： | Qiu Yuyang Qiu Chunhan |
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| 作者单位： | [1]Dept. of Math., Zhejiang Univ., Hangzhou 310027, China. [2]College of Statist. and Math., Zhejiang Gongshang Univ., Hangzhou 310018, China. |
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| 基金项目： | The work of the first author was supported by the Young Talent Foundation of Zhejiang Gongshang University |
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| 摘 要： | The matrix equation AXB = E with the constraint PX=sXP is considered,where P is a given Hermitian matrix satisfying p~2=I and s=±1.By an eigenvalue decomposition of P,the constrained problem can be equivalently transformed to a well-known unconstrained problem of matrix equation whose coefficient matrices contain the corresponding eigenvector, and hence the constrained problem can be solved in terms of the eigenvectors of P.A simple and eigenvector-free formula of the general solutions to the constrained problem by generalized inverses of the coefficient matrices A and B is presented.Moreover,a similar problem of the matrix equation with generalized constraint is discussed.
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| 关 键 词： | 矩阵方程 线性代数 特征值分解 约束问题 存在条件 |
| 收稿时间： | 1 November 2006 |
| 修稿时间： | 2006-11-01 |
Matrix equation <Emphasis Type="Italic">AXB = E</Emphasis> with <Emphasis Type="Italic">PX = sXP</Emphasis> constraint |
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| Qiu Yuyang Qiu Chunhan.MATRIX EQUATION AXB = E WITH PX = sXP CONSTRAINT[J].Applied Mathematics A Journal of Chinese Universities,2007,22(4):441-448. |
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| Authors: | Qiu Yuyang Qiu Chunhan |
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| Abstract: | The matrix equation AXB = E with the constraint PX = sXP is considered, where P is a given Hermitian matrix satisfying P2 = I and s = ±1. By an eigenvalue decomposition of P, the constrained problem can be equivalently transformed to a well-known unconstrained problem of matrix equation whose coefficient matrices contain the corresponding eigenvector, and hence the constrained problem can be solved in terms of the eigenvectors of P. A simple and eigenvector-free formula of the general solutions to the constrained problem by generalized inverses of the coefficient matrices A and B is presented.Moreover, a similar problem of the matrix equation with generalized constraint is discussed. |
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| Keywords: | eigenvalue decomposition constrained problem existence condition form of the solution |
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