2022/09/11 by Shinichi Tajima, Tajima, Shinichi, Katsuyoshi Ohara +3 · 1 citation
Computer Science · Engineering · Mathematics · #15A18 #68W30 #Advanced Optimization Algorithms Research #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Matrix Theory and Algorithms #Photonic and Optical Devices #Rings and Algebras (math.RA) #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.2209.04807
openalex publication_date 2022/09/11 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
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.