Let V be a complex vector space. If $\langle T(v),v\rangle\in \mathbb R$ for every $v \in V$, then is T self adjoint?
30996
If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint
59531
Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
6202
$V$ be a vector space , $T:V \to V$ be a linear operator , then is $\ker (T) \cap R(T) \cong R(T)/R(T^2) $?
47015
Vector Space Structures over ($\mathbb{R}$,+)
83183
Why is $\langle x| x' \rangle=\delta(x-x')$?
128985
Show that $\langle x,y\rangle_A = \langle Ax,Ay\rangle$ is an inner product on $\mathbb R^n$
44685
Inner product on $C(\mathbb R)$
117187
Uniqueness of the involution on a $C^*$-algebra
52198
Why is every selfadjoint operator closed?
60934
What is a complex inner product space "really"?
17748
Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
69766
Is every normed vector space, an inner product space
95481
The set of self-adjoint operators over a Hilbert space doesn't form a lattice
36090
$TT^*=T^2$, show that $T$ is self-adjoint
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
153203
Let $4$ and $5$ be the only eigenvalues of $T$. Show $T^2-9T + 20I = 0$ , T is self adjoint.
146690
Basis for adjoint representation of $sl(2,F)$