In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain.
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.
[3] These transformations are used in signal processing, optics, and quantum mechanics.
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.
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