information:filtering
Operators on inner product spaces

Several types of linear maps A: V → W {\displaystyle A:V\to W} between inner product spaces V {\displaystyle V} and W {\displaystyle W} are of relevance:

From the point of view of inner product space theory, there is no need to distinguish between two spaces which are isometrically isomorphic. The spectral theorem provides a canonical form for symmetric, unitary and more generally normal operators on finite dimensional inner product spaces. A generalization of the spectral theorem holds for continuous normal operators in Hilbert spaces.