Prove que $E$ idempotent is self-adjoint if and only if $EE^*=E^*E$.
99942
A normal, idempotent linear operator must be self-adjoint
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
140724
How to prove two equivalence classes are disjoint?
133884
A proof using Yoneda lemma
5226
Prove that a finite semigroup G with identity is a group if and only if G contains only one idempotent
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
156727
A step in the proof of Characterization of $W^{1,\infty}$
54668
Proof for the completeness of eigenfunctions of a self-adjoint operator
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
55018
Prove that $A^*A + I$ is invertible
119352
compact and self adjoint square root of an operator
144104
Show that a positive operator on a complex Hilbert space is self-adjoint
52198
Why is every selfadjoint operator closed?
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
23946
Prove the definitions of $e$ to be equivalent
103536
How to prove $|e^{i\theta} - 1| \leq |\theta|$?
146730
The adjoint of left exterior multiplication by $\xi$ for hodge star operator