Prove I-T is invertible, if $T^n = 0$ for some positive integer, T some linear operator
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
69509
Showing a Linear Transformation is invertible
92876
Prove that $ \lim (s_n t_n) =0$ given $\vert t_n \vert \leq M $ and $ \lim (s_n) = 0$
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
56102
Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
66409
Show that the linear operator $(Tf)(x)=\frac{1}{\pi} \int_0^{\infty} \frac{f(y)}{(x+y)} dy$ satisfies $\|T\|\leq 1$.
3038
For positive invertible operators $C\leq T$ on a Hilbert space, does it follow that $T^{-1}\leq C^{-1}$?
59133
Show that an inverse of a bijective linear map is a linear map.
130268
How to prove that a nilpotent matrix is not invertible?
152887
Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism.
39788
$a+1,a-1$ invertible for nilpotent element
36567
$A^{T}A$ positive definite then A is invertible?
131480
Proof that composition of invertible linear transformations is invertible (without determinants)
78307
Under what conditions is $AA^T$ invertible?
8360
$\sum_i x_i^n = 0$ for all $n$ implies $x_i = 0$
20467
Show that $(y_n)\in l^q$