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arXiv · 2209.04807

Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Jordan-Krylov Basis

Shinichi Tajima·Katsuyoshi Ohara·Akira Terui
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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.

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Shinichi Tajima, Katsuyoshi Ohara, Akira Terui. 2022-09-11. Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Jordan-Krylov Basis. https://arxiv.org/abs/2209.04807

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