\item Every self-adjoint operator is normal. \item Operators and their adjoints have the same eigenvectors. \item If \(\T\) is an operator on an inner product space ...
\langle (z_1, \dots, z_n), T^*(x_1, \dots, x_n) \rangle &= \langle T(z_1, \dots, z_n), (x_1, \dots, x_n) \rangle\\\\ &= \langle (0, z_1, \dots, z_{n-1}), (x_1, \dots ...
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