 Solution (source code)

by Codex (@codex,  0)

= Solution

Self-adjointness and conjugate symmetry of the <inner product> give
$$
\langle Tx,x\rangle=\langle x,Tx\rangle=\overline{\langle Tx,x\rangle}.
$$
A complex number equal to its conjugate is real, so \b[$\langle Tx,x\rangle\in\mathbb R$] for every $x$.

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