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.
The Spectral Theorem is a fundamental result in linear algebra and functional analysis that pertains to the diagonalization of certain types of matrices and operators. It provides a relationship between a linear operator or matrix and its eigenvalues and eigenvectors.
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