Proving an operator is nilpotent
13346
If $A=AB-BA$, is $A$ nilpotent?
121802
Prove that every self-adjoint unitary linear operator can be expressed in the form $U\alpha = \beta - \gamma$
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
56097
If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent
56102
Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
121100
Rootspaces are $\mathop{ad}$ nilpotent
128361
The kernel and range of the powers of a self-adjoint operator
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
1973
Traces of all positive powers of a matrix are zero implies it is nilpotent
50266
In the following figure prove that: $AK||BC$
156443
if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
28460
Show matrix is nilpotent
61931
Positive operator is bounded
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$