If the inner product of Ax with x is 0 for all x, then A=0.
103142
Question on equivalence of inner product
31766
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
91962
In a ring $a*a=0$ then $a+a=0$
118949
If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$
51483
Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
33989
If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
20921
If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \leq A \leq B$, then det $A \leq$ det $B$.
105141
$\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
98541
If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent
158862
Show that $a(-1) = (-1)a = -a $.
57981
Alternative proof of $a\times0= 0$
14215
Show that the union $\bigcup A_n$ has empty interior in $X$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
38550
2x2 matrices with sum of diagonal entries equal zero
89279
If $\sum a_n/k^n = 0$ for all $k$, then $a_n = 0$ for all $n$