| 多项式Bezout矩阵束 |
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| 引用本文： | 张战英,吴化璋.多项式Bezout矩阵束[J].合肥工业大学学报(自然科学版),2012,35(4):563-566. |
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| 作者姓名： | 张战英 吴化璋 |
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| 作者单位： | 合肥工业大学 数学学院,安徽 合肥,230009 |
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| 基金项目： | 安徽省自然科学基金资助项目 |
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| 摘 要： | 文章利用代数的方法研究了一般基下的多项式Bezout矩阵,从多项式Bezout矩阵和联合友矩阵的块对角化出发,得出了多项式Bezout矩阵与联合友矩阵转置的任意非负整数次幂乘积的块对角化,证明了多项式Bezout矩阵与联合友矩阵的转置的任意非负整数次幂的乘积的线性组合仍是多项式Bezout矩阵,给出了多项式Bezout矩阵束的概念,并用数值例子进行了验证。
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| 关 键 词： | 多项式Bezout矩阵束 生成函数 一般多项式基 |
Polynomial Bezout matrix pencil |
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| ZHANG Zhan-ying
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WU Hua-zhang.Polynomial Bezout matrix pencil[J].Journal of Hefei University of Technology(Natural Science),2012,35(4):563-566. |
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| Authors: | ZHANG Zhan-ying WU Hua-zhang |
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| Institution: | (School of Mathematics,Hefei University of Technology,Hefei 230009,China) |
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| Abstract: | In this paper,the algebraic method is applied in the study of polynomial Bezout matrix with respect to a general polynomial basis.Based on the block diagonalization of polynomial Bezout matrix and confederate matrix,the block diagonalization of the product of polynomial Bezout matrix with arbitrary nonnegative integer power of the transpose of confederate matrix is obtained.It is proved that the linear combination of the product of polynomial Bezout matrix with arbitrary nonnegative integer power of the transpose of confederate matrix is also a polynomial Bezout matrix.Then the concept of polynomial Bezout matrix pencil under a general polynomial basis is induced.Some numerical examples are given to verify the result. |
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| Keywords: | polynomial Bezout matrix pencil generating function general polynomial basis |
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