Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. In spectral theory, the spectral theorem says that if A is an nxn 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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