Relationship between the Karhunen- Loéve transform and the Courant - Fischer theorem (Corresp.)

It is shown that the Karhunen-Loève transform problem can be formulated as a matrix approximation problem with Hilbert-Schmidt error norm. On the other hand, the Courant-Fischer minimax theorem provides a characterization for the best matrix approximation when the spectral norm is used. It appears that the optimality conditions of the Karhunen-Loève problem lead to the selection of a particular solution among the set of solutions to the Courant-Fischer problem.