query: Why $J_k(0)^T$ ~ $J_k(0)$?
positive_passages.docid: 155828
positive_passages.text: How do I show that $A$ and $A^T$ are similar, given that the minimal polynomial of $A$ splits over $\mathbb{F}$?
negative_passages.docid: 25187
negative_passages.text: Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
negative_passages.docid: 133238
negative_passages.text: Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
negative_passages.docid: 36567
negative_passages.text: $A^{T}A$ positive definite then A is invertible?
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: 55377
negative_passages.text: Non-zero eigenvalues of $AA^T$ and $A^TA$
negative_passages.docid: 52791
negative_passages.text: Invertibility of an operator $T$ if $\|I-T\|<1$
negative_passages.docid: 71040
negative_passages.text: If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
negative_passages.docid: 104258
negative_passages.text: Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
negative_passages.docid: 3273
negative_passages.text: Trouble in proving that $\|x\|_p = \max|x_j|$
negative_passages.docid: 6202
negative_passages.text: $V$ be a vector space , $T:V \to V$ be a linear operator , then is $\ker (T) \cap R(T) \cong R(T)/R(T^2) $?
negative_passages.docid: 62192
negative_passages.text: Proof $L{\rm{[}}\frac{{x(t)}}{t}{\rm{] = }}\int_s^\infty {X(u)du} $
negative_passages.docid: 22149
negative_passages.text: How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
negative_passages.docid: 2105
negative_passages.text: $\langle Tu\;|\;u\rangle=0,\;\forall u\in E \Longrightarrow T=0$?
negative_passages.docid: 81040
negative_passages.text: proof about commutative operators and T-cyclic vectors
negative_passages.docid: 142821
negative_passages.text: Why?$\int_0^1\int_{u(t)}^{u(t)+w(t)} f(t,v(t)) dv dt = \int_0^1 f(t,u(t)+\theta w(t))w(t) dt; ~~\theta\in[0,1] $
negative_passages.docid: 34670
negative_passages.text: What exactly is the fixed field of the map $t\mapsto t+1$ in $k(t)$?