If two operators commute, then is it any basis of one of them also a basis of the other?
62845
If two operators commute, does it mean that every eigenfuction of one is also an eigenfunction of the other?
83970
Proof of an elementary property of Projection Operators
36613
Prove that simultaneously diagonalizable matrices commute
108742
Proving commutativity of addition for vector spaces
92314
When does function composition commute?
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
119684
Is a contraction idempotent operator self-adjoint?
85581
Matrices commute if and only if they share a common basis of eigenvectors?
153355
Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?
52935
Do eigenvectors of quantum operators span the whole Hilbert Space?
116517
Is every invertible matrix a change of basis matrix?
67990
Commutativity of matrix and its transpose
105717
Trace of a commutator is zero - but what about the commutator of $x$ and $p$?
19675
Commutator not transitive
57731
Can commuting matrices $X,Y$ always be written as polynomials of some matrix $A$?
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
158355
If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$