Is a complex operator $T$ with $\langle T(v),v \rangle =0$ for all $v$ equal to $0$?
30569
Prove that the only operator on $\mathbb{C}$ for which his inner product is zero is zero
122213
Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
34147
$\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
128875
Expectation values of the position operator is equal to zero in case of even potentials?
2635
equality of two operators...
107450
False proof that $ρe^{iθ} = ρ$ and so complex numbers do not exist?
57166
Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
102871
$\langle r\rangle$ maximal $\iff r$ irreducible
144097
eigenvalues and eigenvectors of $vv^T$
111550
Let $A$ be a square complex matrix of size $n$ then $\langle Ax,x\rangle=0$ for $\forall x \in \Bbb C^n$ $\iff A=0$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
114250
If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$
37867
If $0$ is the only eigenvalue of a linear operator, is the operator nilpotent
48563
If $\Gamma^k_{ij}(p)=0$, then $\nabla_{E_i}E_j (p)=0?$
42334
Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?