query: If $T^m(\alpha)=0,$ with $\alpha \in V$ and $m \in \mathbb{N}$, then $T(\alpha)=0$
positive_passages.docid: 156858
positive_passages.text: Kernel of powers of a normal operator
negative_passages.docid: 57639
negative_passages.text: Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
negative_passages.docid: 48563
negative_passages.text: If $\Gamma^k_{ij}(p)=0$, then $\nabla_{E_i}E_j (p)=0?$
negative_passages.docid: 118949
negative_passages.text: If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$
negative_passages.docid: 158189
negative_passages.text: If $\{E_\alpha\}$ is connected, $\bigcap\limits_{\alpha\in A}E \neq \emptyset$, then $\bigcup\limits_{\alpha\in A}E$ is connected
negative_passages.docid: 92876
negative_passages.text: Prove that $ \lim (s_n t_n) =0$ given $\vert t_n \vert \leq M $ and $ \lim (s_n) = 0$
negative_passages.docid: 62303
negative_passages.text: For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
negative_passages.docid: 20879
negative_passages.text: Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?
negative_passages.docid: 13899
negative_passages.text: Proof that $-v = (-1)*v$
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: 37813
negative_passages.text: If $T\colon \mathbb R^n \to \mathbb R^n $ linear and $T^2 = kT$
negative_passages.docid: 125763
negative_passages.text: If $\mathrm{tr}(A)=0$, then we have $A=BC-CB?$
negative_passages.docid: 103839
negative_passages.text: Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
negative_passages.docid: 109647
negative_passages.text: Ext$_R^n(Q,A)=0=$Tor$_n^R(Q,A)$ where $Q$ is the field of fractions of a domain $R$
negative_passages.docid: 1914
negative_passages.text: General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$
negative_passages.docid: 101467
negative_passages.text: Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.
negative_passages.docid: 39082
negative_passages.text: Proving $x^\alpha-\alpha x \le 1- \alpha $