Spectral theorem (source code)

= Spectral theorem
{title2=$A=\int\lambda\,dE(\lambda)$}
{wiki}

The spectral theorem represents a <normal operator> by multiplication by its spectral parameter. In a finite-dimensional <inner product space>, this is diagonalization in an <orthonormal basis>; for a <self-adjoint operator> on a <Hilbert space>, it uses a <projection-valued measure>. Unbounded operators additionally require their natural square-integrability domain.