$T^*T=TT^*$ and $T^2=T$. Prove $T$ is self adjoint: $T=T^*$
99942
A normal, idempotent linear operator must be self-adjoint
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
26249
Self adjoint operators and trace class property
54217
Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.
151721
Uhlmann's Theorem: proof of $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $
155123
Selfadjoint Operator: Basic Criterion
144097
eigenvalues and eigenvectors of $vv^T$
48524
Existence proof of the tensor product using the Adjoint functor theorem.
54668
Proof for the completeness of eigenfunctions of a self-adjoint operator
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
45998
The range of $T^*$ is the orthogonal complement of $\ker(T)$
28416
Show that $\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$
18379
Linear transformation $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ such that $T^{2}=\lambda T.$
118996
Prove that $T$ is an orthogonal projection
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
82046
prove that this double transpose $T''$ it's not injective.