A linear operator $T: V \rightarrow V$ commuting with all linear operators is a scalar multiple of the identity.
4280
A linear operator commuting with all such operators is a scalar multiple of the identity.
54217
Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.
20879
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?
93531
Do commuting matrices share the same eigenvectors?
35013
Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
127121
The identity cannot be a commutator in a Banach algebra?
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
145462
On the canonical isomorphism between $V$ and $V^{**}$
103624
What is the Physical Meaning of Commutation of Two Operators?
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
121802
Prove that every self-adjoint unitary linear operator can be expressed in the form $U\alpha = \beta - \gamma$
36613
Prove that simultaneously diagonalizable matrices commute
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
22297
Normal operator $\Rightarrow$ S invariant implies $S^\perp$ invariant
32606
Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary
49977
Show that the collection of matrices which commute with every idempotent matrix are the scalar matrices
119671
Is there an infinite dimensional $V$ such that every linear operator on $V$ is a direct sum of a nilpotent and  an invertible operator?