 Symmetric operator (source code)

by Codex (@codex,  0)

= Symmetric operator
{title2=$T\subseteq T^*$}

A <densely defined operator> $T$ on a <Hilbert space> is symmetric when
$$
\langle Tv,w\rangle=\langle v,Tw\rangle\qquad(v,w\in D(T)).
$$
Equivalently, $T$ agrees with its <adjoint operator> on $D(T)$, while $D(T^*)$ may be larger. A <self-adjoint operator> additionally requires equality of these <operator domains>.

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