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We discuss the accurate determination of matrix elements < f| h_w | i > whereneither |i> nor |f> is the vacuum state and h_w is some operator. Usingsolutions of the Generalized Eigenvalue Problem (GEVP) we construct estimatorsfor matrix elements which converge rapidly as a function of the Euclidean timeseparations involved. |i> and |f> may be either the ground state in a givenhadron channel or an excited state. Apart from a model calculation, theestimators are demonstrated to work well for the computation of the B*Bpi-coupling in the quenched approximation. They are also compared to a standardratio as well as to the "summed ratio method" of [1,2,3]. In the model, we alsoillustrate the ordinary use of the GEVP for energy levels.

On the computation of hadron-to-hadron transition matrix elements in lattice QCD