I am trying to find an example of a matrix $B \in Q^{2,2}$ that is diagonalisable if the base field is $R$, but which is not diagonalisable if the base field is $Q$. I am not entirely sure if I am grasping the concepts behind a base field correctly so an explanation would be appreciated.
2026-04-04 01:02:20.1775264540
An example of a matrix $B \in Q^{2,2}$ that is diagonalisable in one field but not another
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