query: How to check $\phi$ is linear?
positive_passages.docid: 24900
positive_passages.text: Homogeneity and Differentiability at $0$ implies linearity?
negative_passages.docid: 63952
negative_passages.text: Disproving: If $(\Gamma\vdash(\phi\,\lor\psi))$, either $(\Gamma\vdash\phi)$ or $(\Gamma\vdash\psi)$ is true
negative_passages.docid: 9753
negative_passages.text: How to solve the equation $\phi(n) = k$?
negative_passages.docid: 119118
negative_passages.text: Prove $n\mid \phi(2^n-1)$
negative_passages.docid: 138819
negative_passages.text: Prove that $\phi(n) \geq \sqrt{n}/2$
negative_passages.docid: 78342
negative_passages.text: When is $\phi(n)$ a prime number?
negative_passages.docid: 36227
negative_passages.text: Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
negative_passages.docid: 121464
negative_passages.text: Linearized equations
negative_passages.docid: 117681
negative_passages.text: For which Natural $n\ge2: \phi(n)=n/2$
negative_passages.docid: 62076
negative_passages.text: Can any channel be written as $\Phi(X)=\operatorname{Tr}_{\mathcal Z}[U(X\otimes \sigma)U^\dagger]$ for any state $\sigma$?
negative_passages.docid: 94558
negative_passages.text: Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
negative_passages.docid: 91087
negative_passages.text: For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?
negative_passages.docid: 126593
negative_passages.text: How to find out whether a transformation is a canonical transformation?
negative_passages.docid: 33518
negative_passages.text: An error formula for linearization
negative_passages.docid: 99105
negative_passages.text: Are the functions $\sin^n(x)$ linearly independent?
negative_passages.docid: 51483
negative_passages.text: Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
negative_passages.docid: 81879
negative_passages.text: $Av=λv$ basis proof problems