  In random-matrix ensembles that interpolate between the three basic ensembles
(orthogonal, unitary, and symplectic), there exist correlations between
elements of the same eigenvector and between different eigenvectors. We study
such correlations, using a remarkable correspondence between the interpolating
ensembles late in the crossover and a basic ensemble of finite size. In small
metal grains or semiconductor quantum dots, the correlations between different
eigenvectors lead to enhanced fluctuations of the electron-electron interaction
matrix elements which become parametrically larger than the non-universal
fluctuations.
