Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Jordan-Krylov Basis
Rings and Algebras
2025-09-16 v5 Symbolic Computation
Commutative Algebra
Abstract
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.
Cite
@article{arxiv.2209.04807,
title = {Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Jordan-Krylov Basis},
author = {Shinichi Tajima and Katsuyoshi Ohara and Akira Terui},
journal= {arXiv preprint arXiv:2209.04807},
year = {2025}
}
Comments
35 pages. The title has been revised to better reflect the scope and contributions of the paper