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.

翻译：为计算一个整数或合理数字矩阵的通用电子空间提议了一个有效的精确方法,我们方法的关键是使用最低限度的灭火多元体和Jourdan-Krylov基础的概念,采用了一种称为Jordan-Krylov消除的新方法来设计计算约旦-Krylov基础的算法,由此得出的算法输出普遍电子空间作为约旦链的一种形式,值得注意的是,在输出中,通用电子元体的成分在相关的电子价值中以多元值作为变量。