Transform theory

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.

pectral 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.

Transforms

Laplace transform

Fourier transform

Mellin transform

Hankel transform

Z-transform

ee also

*Spectral theory
*Laplace transform
*Fourier transform
*Transform (mathematics)

References

*Keener, James P. 2000. "Principles of Applied Mathematics: Transformation and Approximation". Cambridge: Westview Press. ISBN 0-7382-0129-4


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