  To measure an observable of a quantum mechanical system leaves it in one of
its eigenstates and the result of the measurement is one of its eigenvalues.
This process is shown to be a computational resource. It allows one, in
principle, to diagonalize hermitean (N by N) matrices by quantum mechanical
measurements only. To do so, one considers the given matrix as an observable of
a single spin with appropriate length s=(N-1)/2, which can be measured using a
generalized Stern-Gerlach apparatus. Then, each run provides one eigenvalue of
the observable. As it is based on the `collapse of the wave function'
associated with a measurement, the procedure is neither a digital nor an analog
calculation--it defines thus a new quantum mechanical method of computation.
