Let K ⊆ L {\displaystyle {}K\subseteq L} be a field extension. Let an n × n {\displaystyle {}n\times n} -matrix M {\displaystyle {}M} over K {\displaystyle {}K} be given. Show that the minimal polynomial P ∈ K [ X ] {\displaystyle {}P\in K[X]} coincides with the minimal polynomial of M {\displaystyle {}M} , considered as a matrix over L {\displaystyle {}L} .
![{\displaystyle {}P\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4692e3ffcbd66e900f8975113ff3f32f1cabc21a)
