Adjoint operator on a finite dimensional space
45998
The range of $T^*$ is the orthogonal complement of $\ker(T)$
128229
Proving that the transformation obtained from an adjoint pair is natural
92281
Normal Operator that is not Self-Adjoint
36826
Products of Differential Operators
74147
Compactness of  Multiplication Operator on $L^2$
144104
Show that a positive operator on a complex Hilbert space is self-adjoint
16692
a representation condition of Hilbert space
54668
Proof for the completeness of eigenfunctions of a self-adjoint operator
8805
Bounded linear operators that commute with translation
19729
An infinite dimensional limit
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
2129
Showing that the derivative operator is not bounded on $L^2 (\mathbb{R})$
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
123505
how to prove vector norm equivalence in finite dimensional space($\mathbb{R}^{n}$)?
101631
Determinant of a finite-dimensional matrix in terms of trace
82464
$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
11558
How to show that the limit of compact operators in the operator norm topology is compact