A matrix equation Xⁿ = aI

2014/12/30 by Taehyeok Heo, Heo, Taehyeok, Jihoon Choi +3
Computer Science · Mathematics · #15A24 #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1412.8571

openalex publication_date 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a matrix equation Xⁿ = aI. We factorize Xⁿ - aI based upon the factorization of xⁿ - a and then give a necessary and sufficient condition for one of the factors to be the zero matrix.

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