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Operators

Operator (Matrix) properties

U^\dagger is the adjoint of $U$, and in matrix representation is given by $(U^*)^T$, where $^*$ marks the complex conjugate and $^T$ the transpose.
An operator (matrix) $U$ is said to be normal if $U^\dagger U = U U^\dagger$.
- A normal operator is diagonizable (spectral decomposition)
An operator (matrix) $U$ is said to be unitary if $U^\dagger U = I$.
An operator (matrix) $U$ is said to be hermitian if $U = U^\dagger$.
- A hermitian operator is normal.