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transform theory
In mathematics, transform theory is the study of transforms. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or ''diagonalized'' as in spectral theory.
==Spectral theory==
In spectral theory, the spectral theorem says that if ''A'' is an ''n''×''n'' self-adjoint matrix, there is an orthonormal basis of eigenvectors of ''A''. This implies that ''A'' is diagonalizable.
Furthermore, each eigenvalue is real.
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