 Karhunen–Loève expansion

The Karhunen–Loève expansion writes a centered square-integrable random function as $X={\sum }_k{\xi }_k{\varphi }_k$ in mean square, where the ${\varphi }_k$ are principal component functions and the uncorrelated scores satisfy $\mathbb{E}{\xi }_k^2={\lambda }_k$.