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.

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.

Transforms

gollark: `Oh, I set up a nuclear fusion reactor ` ← my clipboard.

gollark: apioform.

gollark: > or is it just special cased for strings for literally no reasonGo is entirely special cases. It has no operator overloading.

gollark: You are so speleological and geomagnetic.

gollark: No. This is simply not acceptable.

References

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.