Transform theory

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. 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. 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.