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| 非线性矩阵方程的一般解(英文) | |
| 引用本文： | 李媛媛,李煜,徐常青.非线性矩阵方程的一般解(英文)[J].广西大学学报(自然科学版),2008,33(1):83-86. |
| 作者姓名： | 李媛媛 李煜 徐常青 |
| 作者单位： | 1. 江汉大学,数计学院,湖北,武汉,430056 2. 海军工程大学,电子工程学院,湖北,武汉,430033 3. 安徽大学,数计学院,安徽,合肥,230039 |
| 基金项目： | Foundation item:Anhui province point item(2006KJ066A) |
| 摘 要： | 与研究m次代数方程相类似地研究了m次非线性矩阵方程,给出了一般解的求法,一般解的结构,一般解的线性组合的性质.当矩阵是非奇异矩阵时,它的m次矩阵根是有限个,特别是一个非奇异的Jordan块的m次矩阵根有m个.当矩阵是奇异矩阵时,它可能有m次矩阵根,也可能没有m次矩阵根,这由它的特征值及对应的Jordan块阶数决定.这种判定方法又直接导出了m次可解矩阵方程根的公式,及非奇异矩阵的m次根的表达式.最后我们也在各种不同的情况给出了结论的数值例子. |
| 关 键 词： | m次矩阵根 非奇异矩阵 线性张成 对角相似 m-root non-singular matrix linear spanning diagonal similar |
| 文章编号： | 1001-7445(2008)01-0083-04 |
| 修稿时间： | 2007年12月20 |
The general solution of Non-linear Matrix Equation |
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| LI Yuan-yuan,LI Yu,XU Chang-qing.The general solution of Non-linear Matrix Equation[J].Journal of Guangxi University(Natural Science Edition),2008,33(1):83-86. | |
| Authors: | LI Yuan-yuan LI Yu XU Chang-qing |
| Institution: | LI Yuan-yuan1,LI Yu2,XU Chang-qing3(1.School of Mathematics , Computational Science,Jiang-Han University,Wuhan,430056,China,3.2.Electronic Engineering College,Naval University of Engineering,wuhan,430033,3.SchoolofMathematics , Computational Science,An-Hui University,Hefei,230039) |
| Abstract: | The general solution of solvable matrix equation Xm=A was obtained. If A is non-singular matrix, the equation Xm=A has finitely many solutions. Specially, the number of the m-root of non-singular Jordan block was m. When the matrix is a singular matrix, it may have m-root, also possible have no m-root. This is determined by their Jordan normal form. And when m is an even number, the solutions of Xm=A span whole Cn×n if and only if A=λI with λ≠0.We also determine the precise number of solutions in various cases. |
| Keywords: | m-root non-singular matrix linear spanning diagonal similar |
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