If X is a Hilbert space .
T is a normal operator , then a remarkable result known as the spectral theorem gives an analogue of the diagonalisation theorem for normal finite - dimensional operators ( Hermitian matrices , for example ) .
If X is a Hilbert space and T is a normal operator , then a remarkable result known as the spectral theorem gives an analogue of the diagonalisation theorem for normal finite - dimensional operators ( Hermitian matrices , for example ) .