query: How do I show that $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $ for general matrices $A$ and $B$?
positive_passages.docid: 151721
positive_passages.text: Uhlmann's Theorem: proof of $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $
negative_passages.docid: 38850
negative_passages.text: How to show Von Neumann Trace inequality $ \text{Tr}(AB) \leq \sum_{i=1}^n \sigma_{A,i}\sigma_{B,i} $?
negative_passages.docid: 25357
negative_passages.text: Matrices $B$ that commute with every matrix commuting with $A$
negative_passages.docid: 128710
negative_passages.text: Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
negative_passages.docid: 65873
negative_passages.text: A proof for Atiyah-Macdonald Exercise I.21.iii
negative_passages.docid: 147564
negative_passages.text: Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
negative_passages.docid: 116558
negative_passages.text: Consider two linear operators $\hat{A}$ and $\hat{B}$. Show that $e^{\hat{A}}e^{\hat{B}}=e^{\hat{A}+\hat{B}}e^{[\hat{A},\hat{B}]/2}$
negative_passages.docid: 7384
negative_passages.text: How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
negative_passages.docid: 101861
negative_passages.text: How do you prove that $tr(B^{T} A )$ is a inner product?
negative_passages.docid: 89533
negative_passages.text: $\mathcal{K}(L^2(\mathbb{R}^m \times \mathbb{R}^n)) = \mathcal{K}(L^2(\mathbb{R}^m)) \otimes \mathcal{K}(L^2(\mathbb{R}^n))$?
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 105363
negative_passages.text: $\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
negative_passages.docid: 78298
negative_passages.text: On the nilpotence of the matrix $AB-BA$
negative_passages.docid: 57318
negative_passages.text: Property of the conjugate transpose matrix with inner product
negative_passages.docid: 98507
negative_passages.text: $\text{Aut}(F)$ is isomorphic to the multiplicative group of all $n\times n$ matrices over $\mathbb Z$
negative_passages.docid: 23224
negative_passages.text: $\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
negative_passages.docid: 90475
negative_passages.text: Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?