1
$\begingroup$

This question already has an answer here:

Assume $K/F$ be a field extension and $A,B \in M_n(F)$ and $P\in GL_n(K)$ such that $PAP^{-1}=B$. Can we find $C\in GL_n(F)$ such that $CAC^{-1}=B$?

$\endgroup$

marked as duplicate by Watson, Dietrich Burde, Arnaud D., TastyRomeo, hardmath Jan 8 '17 at 2:46

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

3
$\begingroup$

Yes, this is true. This is essentially a consequence of the existence and unicity of the Frobenius normal form and from the fact that two matrices over $K$ are conjugated in $M_n(K)$ if and only if they have the same Frobenius normal form.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.