Generalized eigenvalue problems are often solved by a combination of inverse iteration and the Rayleigh–Ritz procedure. In this paper we show that significant advantages can be obtained in this context by applying the Rayleigh–Ritz procedure to an inverted operator, either explicitly while using subspace iteration or implicitly by applying the Lanczos algorithm to the inverted operator. Since the Lanczos algorithm is much more powerful than subspace iteration it should be used whenever possible.