Spectral decomposition is a mathematical process that expresses a self-adjoint operator in terms of its eigenvalues and eigenvectors, allowing it to be represented as a sum of projectors associated with these eigenvalues. This decomposition reveals significant insights about the operator's behavior, such as simplifying calculations and providing a clearer understanding of its structure. The concept is crucial for analyzing the properties of self-adjoint operators, particularly in relation to their spectral properties.
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