Can the minimal polynomial $P$ of a square matrix over some field $F$ have the form $P=Q(X-\lambda)^2$ for some $\lambda \in F$ ?
2026-05-11 09:42:34.1778492554
Can the minimal polynomial of a matrix have a root with multiplicity?
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Any monic polynomial occurs as the minimal polynomial of some square matrix, in particular of its own companion matrix. Therefore, yes, multiple roots are definitely possible for minimal polynomials.