In this paper we perform a spectral analysis for the kernel operator associated with the transition kernel for the Metropolis-Hastings algorithm that uses a fixed, location independent proposal distribution. Our main result is to establish the spectrum of the kernel operator T in the continuous case. In the case of finite state spaces we give the eigenvalues and eigenvectors, thereby filling in a few missing details in the slightly incomplete analysis in Liu
(1996). The spectrum of T is of interest for several reasons. Performance measures such as total variation distance after a finite number of iterations, rate of convergence in total variation norm, acceptance rate, autocovariances and efficiency can be expressed in terms of the spectrum of T.