query: Conjugate in $\mathbb{C}$ implies conjugate in $\mathbb{R}$?
positive_passages.docid: 155275
positive_passages.text: If two real matrices are conjugated over $\mathbb{C}$, are they then also conjugated over $\mathbb{R}$?
negative_passages.docid: 111056
negative_passages.text: Harmonic conjugate of $\ln|z|$ in $\mathbb C \setminus \{0\}$
negative_passages.docid: 11828
negative_passages.text: continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 142174
negative_passages.text: Nonexistence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$
negative_passages.docid: 57269
negative_passages.text: A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$
negative_passages.docid: 117418
negative_passages.text: Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation
negative_passages.docid: 112131
negative_passages.text: Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
negative_passages.docid: 134442
negative_passages.text: Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?
negative_passages.docid: 73927
negative_passages.text: Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
negative_passages.docid: 146028
negative_passages.text: $GL(n, \mathbb{C})$ is isomorphic to a subgroup of $GL(2n, \mathbb{R})$
negative_passages.docid: 42774
negative_passages.text: Examples of involutions on $\mathbb{R}$
negative_passages.docid: 135441
negative_passages.text: When is $\mathbb{Z}[\alpha]$ dense in $\mathbb{C}$?
negative_passages.docid: 143354
negative_passages.text: Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
negative_passages.docid: 1117
negative_passages.text: Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
negative_passages.docid: 112807
negative_passages.text: Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
negative_passages.docid: 5996
negative_passages.text: Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?