论文标题
通过歼灭多项式计算矩阵的通用特征空间的精确算法
Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Annihilating Polynomials
论文作者
论文摘要
提出了一种有效的精确方法，用于计算整数矩阵或有理数矩阵的广义特征空间。我们方法的钥匙是使用最小的歼灭多项式和Jourdan-Krylov基础的概念。引入了一种称为Jordan-Krylov消除的新方法，用于设计用于计算Jordan-Krylov基础的算法。所得算法将广义特征空间作为约旦链的一种形式。值得注意的是，在输出中，广义特征向量的组成部分表示为相关特征值中的多项式作为变量。
An effective exact method is proposed for computing generalized eigenspaces of a matrix of integers or rational numbers. Keys of our approach are the use of minimal annihilating polynomials and the concept of the Jourdan-Krylov basis. A new method, called Jordan-Krylov elimination, is introduced to design an algorithm for computing Jordan-Krylov basis. The resulting algorithm outputs generalized eigenspaces as a form of Jordan chains. Notably, in the output, components of generalized eigenvectors are expressed as polynomials in the associated eigenvalue as a variable.
