Sselfadjointness
Selfadjointness is a property of linear operators acting on Hilbert spaces. A linear operator $A$ on a Hilbert space $H$ is called selfadjoint if its domain $D(A)$ is equal to its domain of definition $D(A^*)$, and for all vectors $u, v$ in $D(A)$, the following equality holds: $\langle Au, v \rangle = \langle u, Av \rangle$. Here, $A^*$ denotes the adjoint of the operator $A$, and $\langle \cdot, \cdot \rangle$ represents the inner product of the Hilbert space.
In simpler terms, a selfadjoint operator is one that is equal to its own adjoint. This property
The condition that $D(A) = D(A^*)$ is important because the adjoint operator $A^*$ might be defined on