  A spectral characterization of the matching number (the size of a maximum
matching) of a graph is given. More precisely, it is shown that the graphs G of
order n whose matching number is k are precisely those graphs with the maximum
skew rank 2k such that for any given set of k distinct nonzero purely imaginary
numbers there is a real skew-symmetric matrix A with graph G whose spectrum
consists of the given k numbers, their conjugate pairs, and n-2k zeros.
