  A graph is called $k$-extendable if each $k$-matching can be extended to a
perfect matching. We give spectral conditions for the $k$-extendability of
graphs and bipartite graphs using Tutte-type and Hall-type structural
characterizations. Concretely, we give a sufficient condition in terms of the
spectral radius of the distance matrix for the $k$-extendability of a graph and
completely characterize the corresponding extremal graphs. A similar result is
obtained for bipartite graphs.
