query: Does $U(A)$ and $A^{\mu}_{\nu}$ commute?
positive_passages.docid: 151347
positive_passages.text: Why do operators belonging to different Hilbert spaces commute?
negative_passages.docid: 84984
negative_passages.text: What does $\partial_{\mu}$ mean?
negative_passages.docid: 27821
negative_passages.text: A problem on rank of $A$ and $\operatorname{adj}(A)$
negative_passages.docid: 158082
negative_passages.text: Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
negative_passages.docid: 66610
negative_passages.text: Finding a correspondence between $\{0,1\}^A$ and $\mathcal P(A)$
negative_passages.docid: 42334
negative_passages.text: Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
negative_passages.docid: 84
negative_passages.text: For what $n$ is $U_n$ cyclic?
negative_passages.docid: 62506
negative_passages.text: Why $SU(3)$ and not $U(3)$?
negative_passages.docid: 114626
negative_passages.text: Lie Algebra of U(N) and SO(N)
negative_passages.docid: 50130
negative_passages.text: $\operatorname{Aut}(V)$ is isomorphic to $S_3$
negative_passages.docid: 22149
negative_passages.text: How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
negative_passages.docid: 45179
negative_passages.text: When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
negative_passages.docid: 34147
negative_passages.text: $\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
negative_passages.docid: 121198
negative_passages.text: $W^{1,1}(\mathbb{R}^n)$ is not compactly embedded in $L^1(\mathbb{R}^n)$?
negative_passages.docid: 65062
negative_passages.text: Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
negative_passages.docid: 41385
negative_passages.text: $\nabla U=0 \implies U=\mathrm{constant}$ only if $U$ is defined on a connected set?
negative_passages.docid: 28565
negative_passages.text: Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$