query: $\chi_A(\lambda)=\lambda^n -Tr(A)\lambda^{n-1}+...+(-1)^ndet(A) \implies \chi_{A^{-1}}? $
positive_passages.docid: 149364
positive_passages.text: Characteristic polynomial of an inverse
negative_passages.docid: 86919
negative_passages.text: When (and more importantly, why) does $AA^T$ have an inverse?
negative_passages.docid: 95106
negative_passages.text: If $Y|X \sim \mathcal{N}(0,1)$ then is $Y^2|X \sim \chi^2(1)$?
negative_passages.docid: 147659
negative_passages.text: Counterexample to "if $f:A\to A$ induces the identity $\hat f:\operatorname{Spec}(A)\to\operatorname{Spec}(A)$, then $f=\operatorname{id}_A$"
negative_passages.docid: 42334
negative_passages.text: Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
negative_passages.docid: 153448
negative_passages.text: Show that $A\in\mathbb{C}_n$ is normal $\iff$ $tr(A*A) = \sum_{i = 1}^n|\lambda_i|^2$, where $\lambda_1,...,\lambda_n$ are the eigenvalues of $A$.
negative_passages.docid: 111515
negative_passages.text: Proving that $-a=(-1)\cdot a$
negative_passages.docid: 70304
negative_passages.text: Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
negative_passages.docid: 36567
negative_passages.text: $A^{T}A$ positive definite then A is invertible?
negative_passages.docid: 51769
negative_passages.text: If $x,y,z\in[-1,1]$ and $1+2xyz\geq x^2+y^2+z^2$, then can we infer $1+2(xyz)^n\geq x^{2n}+y^{2n}+z^{2n}$?
negative_passages.docid: 56102
negative_passages.text: Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
negative_passages.docid: 151805
negative_passages.text: Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$
negative_passages.docid: 108633
negative_passages.text: Why $f^{-1}(f(A)) \not= A$
negative_passages.docid: 81868
negative_passages.text: How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
negative_passages.docid: 142168
negative_passages.text: can we a prove ⊢ (α → α) → (α → α)
negative_passages.docid: 130253
negative_passages.text: Differentiating $\mbox{tr} (ABA^TC)$ w.r.t. $A$
negative_passages.docid: 21553
negative_passages.text: Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$