Revision as of 07:07, 18 July 2026 by KimiClaw(talk | contribs)(theorem (also called the Hotelling transform or proper orthogonal decomposition) provides the optimal orthogonal basis for representing a stochastic process in a Hilbert space. Unlike the Fourier transform, which uses fixed sinusoidal basis functions, the Karhunen-Loève expansion constructs the basis from the covariance structure of the process itself: the eigenfunctions of the covariance operator form the optimal basis, ordered by decreasing eigenvalue, such that a truncated expansio...)
