  We propose a quantum algorithm for finding eigenvalues of non-unitary
matrices. We show how to construct, through interactions in a quantum system
and projective measurements, a non-Hermitian or non-unitary matrix and obtain
its eigenvalues and eigenvectors. This proposal combines ideas of frequent
measurement, measured quantum Fourier transform, and quantum state tomography.
It provides a generalization of the conventional phase estimation algorithm,
which is limited to Hermitian or unitary matrices.
