query: Assume $K/F$ be a field extension and $A,B \in M_n(F)$ . If $A,B$ be conjugate in $GL_n(K)$, is it true that $A,B$ are conjugate in $GL_n(F)$?
positive_passages.docid: 57515
positive_passages.text: Similar matrices and field extensions
negative_passages.docid: 78561
negative_passages.text: Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
negative_passages.docid: 80295
negative_passages.text: Field extensions and algebraic/transcendental elements
negative_passages.docid: 99938
negative_passages.text: Is the conjugation map always an isomorphism?
negative_passages.docid: 98352
negative_passages.text: If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
negative_passages.docid: 93328
negative_passages.text: $\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
negative_passages.docid: 13606
negative_passages.text: Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
negative_passages.docid: 68790
negative_passages.text: Do we have $K(\beta)=K(\beta^2)$ for field extension of odd degree?
negative_passages.docid: 25793
negative_passages.text: Extension fields isomorphic to fields of matrices
negative_passages.docid: 127796
negative_passages.text: Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
negative_passages.docid: 145140
negative_passages.text: Subfield of $\mathbb{Q}(\sqrt[n]{a})$
negative_passages.docid: 42652
negative_passages.text: Must $k$-subalgebra of $k[x]$ be finitely generated?
negative_passages.docid: 131943
negative_passages.text: How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
negative_passages.docid: 78580
negative_passages.text: Is $SL_n(\mathbb{R})$ a normal subgroup in $GL_n(\mathbb{R})$?
negative_passages.docid: 7418
negative_passages.text: The Center of $\operatorname{GL}(n,k)$
negative_passages.docid: 97024
negative_passages.text: If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.
negative_passages.docid: 41815
negative_passages.text: Galois extension of intersection of fields