====== Operators ======
===== Hilbert Space =====
The **Hilbert Space** is an inner product space, which is complete with respect to the norm defined by the inner product.

See also [[https://www.quantiki.org/wiki/hilbert-spaces | on Quantiki]]


===== 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.