The spectral theorem for normal operators states that any normal operator on a finite-dimensional inner product space can be represented as a sum of projections onto orthogonal eigenspaces, where the operator can be diagonalized in an orthonormal basis of eigenvectors. This means that normal operators, which include self-adjoint and unitary operators, possess a well-defined structure in terms of their eigenvalues and eigenvectors. The theorem provides crucial insights into the behavior and properties of these operators, allowing for easier computations and deeper understanding of linear transformations in Hilbert spaces.
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