A matrix equation $X^n = aI$
Taehyeok Heo, Jihoon Choi, and Suh-Ryung Kim
TL;DR
This paper investigates the solutions of the matrix equation X^n = aI by factorizing the polynomial X^n - aI and establishing conditions for solutions based on polynomial factorization.
Contribution
It provides a new factorization approach for the matrix equation X^n = aI and characterizes solutions through necessary and sufficient conditions.
Findings
Factorization of X^n - aI based on polynomial roots
Necessary and sufficient conditions for solutions
Insight into matrix equations of the form X^n = aI
Abstract
In this paper, we study a matrix equation . We factorize based upon the factorization of and then give a necessary and sufficient condition for one of the factors to be the zero matrix.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · Advanced Optimization Algorithms Research